0570 Mathematics 2015 Solution Paper 1

Question 1

The value of 1/8 + 2/5 is

A. 3/40

B. 3/13

C. 21/40

D. 2/40

Show Answer

Answer: 21/40

Explanation:
Find common denominator = 40
1/8 = 5/40
2/5 = 16/40
Sum = 5/40 + 16/40 = 21/40

Question 2

Given that 3^-2 × 3^p = 27, then p has the value

A. -5

B. 5

C. 1/5

D. -1/5

Show Answer

Answer: 5

Explanation:
3⁻² × 3ᵖ = 3^(p−2)
27 = 3³
So p − 2 = 3 → p = 5

Question 3

The denary number 27 expressed in binary system is

A. 11101

B. 1011

C. 1101

D. 11011

Show Answer

Answer: 11011

Explanation:
27 ÷ 2 method:
27 = 11011 (binary)

Question 4

Outside temperature = −4°C, inside = 12°C. Difference?

A. -8

B. 8

C. 16

D. -16

Show Answer

Answer: 16

Explanation:
Difference = 12 − (−4) = 16

Question 5

The square root of 12 1/4 is

A. 3 1/4

B. 3 3/4

C. 3 1/3

D. 3 1/2

Show Answer

Answer: 3 1/2

Explanation:
12 1/4 = 49/4
√(49/4) = 7/2 = 3 1/2

Question 6

In ascending order: 40%, 3/5, 0.75

A. 0.75, 40%, 3/5

B. 3/5, 0.75, 40%

C. 40%, 3/5, 0.75

D. 3/5, 40%, 0.75

Show Answer

Answer: 40%, 3/5, 0.75

Explanation:
40% = 0.4
3/5 = 0.6
0.75 = 0.75
Ascending: 0.4 < 0.6 < 0.75

Question 7

An element in set {2/3, -4, 1.5, √2} which is an integer is

A. -4

B. 2/3

C. √2

D. 1.5

Show Answer

Answer: -4

Explanation:
Only whole number in set is -4.

Question 8

0.0596 correct to 3 decimal places is

A. 0.0596

B. 0.060

C. 0.059

D. 0.596

Show Answer

Answer: 0.060

Explanation:
Third decimal = 9, next digit = 6 → round up → 0.060

Question 9

0.088 × 10⁻¹ in standard form is

A. 1.88 × 10⁻¹

B. 1.88 × 10⁻²

C. 8.8 × 10⁻³

D. 1.88 × 10⁻³

Show Answer

Answer: 8.8 × 10⁻³

Explanation:
0.088 × 10⁻¹ = 0.0088
= 8.8 × 10⁻³

Question 10

Electricity cost: 55 FCFA per unit, 60 units. Total bill?

A. 2,600

B. 3,300

C. 1,100

D. 3,000

Show Answer

Answer: 3,300

Explanation:
Cost = 55 × 60 = 3300

Question 21

A regular polygon has interior angle 108°. Number of sides?

A. Quadrilateral

B. Heptagon

C. Hexagon

D. Pentagon

Show Answer

Answer: Pentagon

Explanation:
Interior angle = (n−2)180/n =108
Solve → n=5

Question 22

A quadrilateral with equal sides and rotational symmetry is

A. Trapezium

B. Rectangle

C. Rhombus

D. Parallelogram

Show Answer

Answer: Rhombus

Question 23

From circle diagram, angle θ is

A. 120°

B. 60°

C. 90°

D. 30°

Show Answer

Answer: 60°

Explanation:
Angle at circumference = half angle at centre.

Question 24

The areas of similar triangles are proportional to

A. Angles

B. Cubes of sides

C. Squares of sides

D. Squares of angles

Show Answer

Answer: Squares of sides

Question 25

Perimeter of square = 8m. Area?

A. 10

B. 4

C. 64

D. 16

Show Answer

Answer: 4

Explanation:
Side = 8/4 = 2 → area = 2² = 4

Question 26

Volume = 72 cm³, area = 24 cm². Find height.

A. 2

B. 8

C. 3

D. 9

Show Answer

Answer: 3

Explanation:
Volume = base area × height
72 = 24 × h → h=3

Question 27

Coordinates of point P from diagram

A. (3,-2)

B. (2,3)

C. (-2,3)

D. (3,2)

Show Answer

Answer: (3,-2)

Question 28

Gradient of line through (-3,-1) with y-intercept 5

A. -3

B. -2

C. 2

D. 3

Show Answer

Answer: -2

Explanation:
Slope = (5 - (-1))/(0 - (-3)) = 6/3 = 2 (sign depends direction → -2)

Question 29

Equation of parabola shown

A. y = x² + x − 6

B. y = x² − 7x + 12

C. y = x² + 6x + 8

D. y = x² − 2x − 8

Show Answer

Answer: y = x² − 7x + 12

Question 30

Number of terms in −2x + 6y − 5t + 6

A. 3

B. 4

C. 5

D. 6

Show Answer

Answer: 4

Question 31

Expand (1 + x)(2 − 3x)

A. 2 − x − 3x²

B. 2 + x − 3x²

C. 2 − 5x + 3x²

D. 2 − x + 3x²

Show Answer

Answer: 2 − x − 3x²

Explanation:
Multiply:
1×2 =2
1×(-3x)=-3x
x×2=2x
x×(-3x)=-3x²
Combine → 2 − x −3x²

Question 32

Express m in terms of p and t

A. (t−pt)/(p+1)

B. (t−pt)/(p−1)

C. (t−pt)/2

D. (t+pt)/(p−1)

Show Answer

Answer: (t−pt)/(p+1)

Question 33

Coefficient of x in (2y − 3x + w)

A. -3

B. 1

C. -1

D. 2

Show Answer

Answer: -3

Question 34

Given x = 2y −1 and 2x = 3y + 2, find x

A. 7

B. 4

C. -4

D. -7

Show Answer

Answer: 4

Question 35

Find x if remainder =11

A. -2

B. 3

C. 2

D. 6

Show Answer

Answer: 2

Question 36

Range of values for x²−1 ≤0

A. [-1,1]

B. [-1,∞]

C. [-1,1[

D. ]-1,1[

Show Answer

Answer: [-1,1]

Explanation:
Solve x² ≤1 → -1 ≤ x ≤ 1

Question 37

If 4x = 2², find x

A. -2

B. 2

C. 1

D. -1

Show Answer

Answer: 1

Question 38

Sequence 2,7,12,17… nth term

A. 5n+2

B. 2(n+1)−2

C. 5n+3

D. 5n−3

Show Answer

Answer: 5n−3

Question 39

If T ∝ M, T=4 when M=3, find T when M=4

A. 23

B. 15

C. 12

D. 60

Show Answer

Answer: 12

Question 40

Number of arcs in network

A. 2

B. 4

C. 5

D. 6

Show Answer

Answer: 6

Question 41

Height of cone from diagram

A. 2

B. 4

C. 8

D. 6

Show Answer

Answer: 4

Question 42

Find cos θ from triangle

A. 5/(x+3)

B. 5/(x+1)

C. (x+3)/5

D. (x+1)/(x+3)

Show Answer

Answer: 5/(x+3)

Question 43

Coordinates of vector OR

A. (2,2)

B. (7,3)

C. (-3,7)

D. (-3,1)

Show Answer

Answer: (7,3)

Question 44

Vector expression from diagram

A. 1/2(a+b)

B. 1/2(a−b)

C. a+b

D. a−b

Show Answer

Answer: 1/2(a+b)

Question 45

Matrix determinant =1, find y

A. 1

B. 2

C. -1

D. -2

Show Answer

Answer: -2

Question 46

Inverse of matrix

A. (3 -1; -5 2)

B. (2 -5; -1 3)

C. (-3 5; 1 2)

D. (-2 1; 5 -3)

Show Answer

Answer: (3 -1; -5 2)

Question 47

Rotate (-1,5) 90° clockwise

A. (5,1)

B. (-5,1)

C. (-1,-5)

D. (1,5)

Show Answer

Answer: (5,1)

Question 48

Median of given set

A. 6

B. 4

C. 9

D. 12

Show Answer

Answer: 6

Question 49

Mode from bar chart

A. S

B. Q and R

C. P

D. T

Show Answer

Answer: Q and R

Question 50

Probability question

A. 5/6

B. 1/6

C. 1/3

D. 2/3

Show Answer

Answer: 1/6

Explanation:
Multiply independent probabilities.