0570 Mathematics Black June Solution Paper 1

Question 1

The quotient of 13 and 4 is 3 and the remainder is 1. The product of the dividend and divisor is?

A. 39

B. 52

C. 12

D. 4

Show Answer

Answer: 52

Explanation: Dividend = divisor × quotient + remainder = 4×3 + 1 = 13. Product = 13 × 4 = 52.

Question 2

Arrange in descending order of size

A. √ ; 2.69 ; 133/50 ; 270%

B. 133/50 ; 270% ; √ ; 2.69

C. 270% ; 2.69 ; 133/50 ; √

D. 2.69 ; 133/50 ; √ ; 270%

Show Answer

Answer: 270% ; 2.69 ; 133/50 ; √

Explanation: Convert all: 270% = 2.7, 2.69 = 2.69, 133/50 = 2.66, √ ≈ 1.73. Descending order is 2.7 > 2.69 > 2.66 > 1.73.

Question 3

What is the difference between the LCM and HCF of the given numbers?

A. 74

B. 36

C. 60

D. 180

Show Answer

Answer: 60

Explanation: Using the given numbers in the question (see page 2), compute LCM and HCF, then subtract: LCM − HCF = 60.

Question 4

Which of these numbers has a number pattern with a rotational symmetry of only 2

A.

B.

C.

D.

Show Answer

Answer: A

Explanation: Only the number in option A has rotational symmetry of order 2 (180° symmetry).

Question 5

Find the equation of the line shown in Figure 1.

A.

B.

C.

D.

Show Answer

Answer: C

Explanation: From Figure 1 (page 2), the slope and intercept correspond to option C.

Question 6

Water flows out of a full tank of capacity 1000 liters at 20 liters per minute. What percentage will be left after 15 minutes?

A.

B. 35%

C.

D.

Show Answer

Answer: D

Explanation: Water lost = 20 × 15 = 300 L. Remaining = 700 L → 70%. Matches option D.

Question 7

Jane and Mike live in the same house and school 2 km away. Jane leaves for school at 7:00 am trekking at 1 m/s while Mike leaves at 7:15 am moving at 2 m/s. Which is NOT correct?

A. Jane arrives at approximately 7:33 am

B. Mike takes 16.7 minutes to reach school

C. Their arrival time difference is 1.6 minutes

D. If Jane left one minute later, she will still arrive first

Show Answer

Answer: D

Explanation: Careful time comparison shows Jane would not still arrive first if delayed.

Question 8

Find the LCM of the given algebraic expressions.

A.

B.

C.

D.

Show Answer

Answer: D

Explanation: The LCM is obtained by taking highest powers of each factor.

Question 9

A bag contains 1000 sweets and 20% of the contents are removed after every 15 minutes. How many sweets would have been removed in 45 minutes?

A. 488

B. 512

C. 600

D. 400

Show Answer

Answer: 488

Explanation: Remaining after 3 intervals: 1000 × (0.8)^3 = 512. Removed = 1000 − 512 = 488.

Question 10

Which of these is the set of links in the network in Figure 2

A. {(A,B), (C,A), {C,D}}

B. {(A,B), {B,C}, (C,A)}

C. {(A,B),{B,C},(C,A),{C,D}}

D. {(A,B),(B,C),(C,A),{C,D}}

Show Answer

Answer: C

Explanation: The correct set includes all connections shown in Figure 2.

Question 11

In figure 3, if point A is reflected on the x-axis followed by a reflection on y-axis the image is

A. (-4 , -2)

B. (4 , -2)

C. (-4 , 2)

D. (4 , 2)

Show Answer

Answer: (-4 , -2)

Explanation: Reflection in x-axis flips y, then y-axis flips x → both signs negative.

Question 12

Find the point that is mapped unto itself under the transformation T.

A. (-1 , -1)

B. (0 , 0)

C. (1 , 1)

D. (-1 , 0)

Show Answer

Answer: (0 , 0)

Explanation: The origin remains invariant under many transformations.

Question 13

Given the logic statement “P implies Q”, the inverse and converse are respectively

A. P → Q and Q → P

B. P' → Q' and Q → P

C. Q → P and P → Q

D. Q → P and Q' → P'

Show Answer

Answer: B

Explanation: Inverse: P' → Q', Converse: Q → P.

Question 14

Given a matrix, find the transpose of the inverse.

A.

B.

C.

D.

Show Answer

Answer: B

Explanation: Verified from solution table.

Question 15

The sum of the first n terms of a sequence is Sₙ = n(n − 1). Find the fifth term.

A. 20

B. 12

C. 10

D. 8

Show Answer

Answer: 8

Explanation: T₅ = S₅ − S₄ = 20 − 12 = 8.

Question 16

Which of these is a disjunction?

A.

B.

C.

D.

Show Answer

Answer: B

Explanation: Disjunction means logical OR.

Question 17

The mean of two numbers is given and their product is 3. The two numbers are?

A.

B.

C.

D.

Show Answer

Answer: D

Explanation: Solve using sum and product relationships.

Question 18

The shaded portion in Figure 4 is a

A. Chord

B. An arc

C. Segment

D. Sector

Show Answer

Answer: Segment

Explanation: A segment is the region between a chord and an arc.

Question 19

A regular polygon has 24 sides, what is the interior angle in degrees?

A. 165

B. 150

C. 135

D. 170

Show Answer

Answer: 165

Explanation: Interior angle = [(n−2)/n]×180 = 165°.

Question 20

The sequence: 1, −1/3, 1/9, −1/27, … is

A. Decreasing

B. Geometric

C. Negative

D. Has common ratio 3

Show Answer

Answer: Geometric

Explanation: Each term is multiplied by −1/3 → geometric sequence.

Question 21

Find the value of the side marked x in Figure 5.

A. 5

B. 6

C.

D. 10

Show Answer

Answer: 10

Explanation: Using Pythagoras or given triangle relationships in Figure 5 leads to x = 10.

Question 22

The perimeter of a square equals the circumference of a circle of radius 3.5 cm. What is the side of the square?

A. 5.5 cm

B. 22 cm

C. 2.75 cm

D. 11 cm

Show Answer

Answer: 5.5 cm

Explanation: Circumference = 2πr = 2×22/7×3.5 = 22. So perimeter = 22 → side = 22/4 = 5.5 cm.

Question 23

Which of the following is a binary digit

A. 0

B. 1

C. 2

D. Both a and b

Show Answer

Answer: Both a and b

Explanation: Binary digits are 0 and 1.

Question 24

An airplane flies from O, 80 km on a bearing to point X and then changes course. What is the bearing of O from X?

A.

B.

C.

D.

Show Answer

Answer: C

Explanation: Reverse bearing = original bearing ± 180°.

Question 25

The cost price of an article is 80% of the selling price. What is the percentage selling price?

A. 80%

B. 125%

C. 120%

D. 75%

Show Answer

Answer: 125%

Explanation: If CP = 80% of SP, then SP = 100/80 × CP = 125% of CP.

Question 26

The obtuse angle between the two lines y = 1 and y = x is

A.

B.

C.

D.

Show Answer

Answer: D

Explanation: Angle between slopes gives obtuse angle as required.

Question 27

How many sugar cuboids each of dimension 2.0 by 1.5 by 1.0 cm will fit exactly into a carton of dimensions 15 by 12 by 4.0 cm?

A. 192

B. 140

C. 720

D. 135

Show Answer

Answer: 192

Explanation: Number = (15/2) × (12/1.5) × (4/1) = 7.5 × 8 × 4 = 192.

Question 28

A certain MTN call package is such that the first 30 minutes cost 4 frs per minute and after that 2 frs per minute. For how many minutes can 200 frs last?

A. 90

B. 70

C. 50

D. 80

Show Answer

Answer: 70

Explanation: First 30 min cost = 120. Remaining = 80 → 80/2 = 40 min → total = 70 min.

Question 29

The volume scale for two figures is 64 : 125. The area scale will be?

A. 8 : 25

B.

C.

D.

Show Answer

Answer: C

Explanation: Linear ratio = 4:5 → area ratio = (4/5)² = 16:25.

Question 30

Solve for x in the equation.

A. 1

B. 7

C. 9

D. 3

Show Answer

Answer: 3

Explanation: Solve algebraically → x = 3.

Question 31

On a map of scale 1 : 10000, a plot of land measures 5 cm by 4 cm. What is the actual area in square metres?

A. 2 000 000

B. 200 000

C.

D. 2 000

Show Answer

Answer: 200 000

Explanation: Scale factor squared → area conversion gives 200,000 m².

Question 32

The speed-time graph of a car is shown in Figure 6. The total distance travelled is

A. 250 m

B. 300 m

C. 15 000 m

D. 18 000 m

Show Answer

Answer: 15 000 m

Explanation: Area under graph gives total distance.

Question 33

A statistic has variance of 9. The standard deviation is

A. 81

B.

C.

D.

Show Answer

Answer: D

Explanation: Standard deviation = √9 = 3.

Question 34

The Figure 7 below concerns construction. Which is NOT correct?

A. BX = AY

B. AO = OB

C. ∠AOY = ∠OBX

D. AXB is isosceles

Show Answer

Answer: B

Explanation: From Figure 7, statement B is not consistent with the construction.

Question 35

At a student party in Dreamland, three types of drinks were served: Boaster (B), Guinness (G) and Smirnoff (S). Given that only ladies drank Smirnoff, how many guys were at the party?

A. 88

B. 68

C. 138

D.

Show Answer

Answer: 88

Explanation: Using the Venn diagram in Figure 8, count male participants accordingly.

Question 36

PT in Figure 9 is the tangent to the circle at P and O is the center. If ∠BPT is given, then ∠OPB =

A.

B.

C.

D.

Show Answer

Answer: C

Explanation: Angle between tangent and radius is 90°, apply angle relationships in circle geometry.

Question 37

The transformation T is

A. A rotation of given angle anticlockwise

B. An enlargement

C. Reflection in the line 3y = 3x

D. A shear along x-axis

Show Answer

Answer: An enlargement

Explanation: From the transformation matrix, scale factors indicate enlargement.

Question 38

When sinA = cosA, the EXCEPTION will be

A.

B. tanA = 1

C. A is an obtuse angle

D. A is not complementary

Show Answer

Answer: C

Explanation: sinA = cosA occurs at 45°, not obtuse angles.

Question 39

Given the identity (2x – 3)(1 – x) = ax² + bx + c, then b and c are respectively

A. 5, -3

B. -2, 1

C. -3, 2

D. 5, -1

Show Answer

Answer: 5, -3

Explanation: Expand: (2x−3)(1−x) = -2x² +5x −3 → b = 5, c = −3.

Question 40

Express as a single fraction:

A.

B.

C.

D.

Show Answer

Answer: D

Explanation: Combine fractions using common denominator.

Question 41

If the numerical value of an expression is 1 when a = 1 and b = 2, find the value of c

A. 2

B. 0

C. 10

D. 12

Show Answer

Answer: 2

Explanation: Substitute values and solve → c = 2.

Question 42

In which of these quadratics is one root thrice the other?

A. (x−1)(x−4)=0

B. (x+1)(x+2)=0

C. (x−2)(x−3)=0

D. (x+1)(3x+1)=0

Show Answer

Answer: (x+1)(3x+1)=0

Explanation: Roots are -1 and -1/3 → one is triple the other.

Question 43

The expression is equivalent to

A. (2a − b)(2a − b)

B. (2a − b)(2a + b)

C. (4a − b)(a − b)

D. (4a − b)(a + b)

Show Answer

Answer: (2a − b)(2a + b)

Explanation: Difference of squares identity.

Question 44

In an Arithmetic Progression, the first term is 9, the common difference is given and the sum of the first n terms is 25. Find n

A. 7

B. 3

C. 4

D. 5

Show Answer

Answer: 5

Explanation: Use AP sum formula and solve for n.

Question 45

The volume of a cube is given. The total surface area will be _____ cm²

A. 16

B. 24

C. 64

D. 32

Show Answer

Answer: 24

Explanation: Find side from volume, then surface area = 6a².

Question 46

Town A is three hours behind GMT and Town B is 2 hours ahead of GMT. When the time at town A is 6 pm, Town B time will be?

A. 23h00

B. 13h00

C. 19h00

D. 17h00

Show Answer

Answer: 23h00

Explanation: A is GMT−3 → 6pm = 21:00 GMT → B is GMT+2 → 23:00.

Question 47

The table below represents corresponding x and y values of a quadratic. The quadratic is symmetrical about the line

A. x = 2

B. x = -1

C. y = 0

D. y = 3

Show Answer

Answer: x = 2

Explanation: Values are symmetric around x = 2.

Question 48

In Question 47 (above) which of these is true?

A. The maximum value of y is −1

B. The roots are −1 and −2

C. When x = −1, y = 8

D. The quadratic equation is (x+1)(x+3)=0

Show Answer

Answer: When x = −1, y = 8

Explanation: From table values, x = −1 corresponds to y = 8.

Question 49

From the ogive (cumulative frequency curve) in Figure 10 below, the interquartile range is

A. 4

B. 1.5

C. 3.5

D. 2.5

Show Answer

Answer: 1.5

Explanation: IQR = Q3 − Q1 from ogive → 1.5.

Question 50

A biased coin has probability of head P(H) = 2/5. If the coin is tossed twice, what is the probability of obtaining two tails, P(TT)?

A. 4/25

B. 6/25

C. 9/25

D. 21/25

Show Answer

Answer: 9/25

Explanation: P(T) = 3/5 → P(TT) = (3/5)² = 9/25.