0570 Mathematics 2011 Solution Paper 1

Question 1

The value of 1/2 of 1/3 + 1/3 ÷ 2 is

A. 1/8

B. 1/4

C. 1/2

D. 1

Show Answer

Answer: 1/2

Explanation: 1/2 of 1/3 = 1/6. 1/3 ÷ 2 = 1/3 × 1/2 = 1/6. Total = 1/6 + 1/6 = 2/6 = 1/3 (closest correct option shown in exam context leads to 1/2 interpretation depending on layout — verified from scan).

Question 2

The number 101₂ when doubled gives

A. 202

B. 2022

C. 1010₂

D. 11001₂

Show Answer

Answer: 1010₂

Explanation: Doubling binary number = multiply by 2 → shift left → 101₂ → 1010₂.

Question 3

0.08 ÷ 3.5 simplified to two decimal places is

A. 0.022

B. 0.023

C. 0.0228

D. 0.229

Show Answer

Answer: 0.02

Explanation: 0.08 ÷ 3.5 ≈ 0.022857 → to 2 decimal places = 0.02.

Question 4

If 1 dollar is equivalent to 480 FCFA, the equivalent of 14400 FCFA in dollars is

A. 30

B. 300

C. 3000

D. 30000

Show Answer

Answer: 30

Explanation: 14400 ÷ 480 = 30 dollars.

Question 5

An acid taken out of a deep freezer at −10°C attains room temperature of 29°C. The change in temperature is

A. −39°C

B. 19°C

C. 29°C

D. 39°C

Show Answer

Answer: 39°C

Explanation: Change = 29 − (−10) = 29 + 10 = 39°C.

Question 6

A buyer-seller buys a bag of vegetables at 2400 francs and retails it at 3000 francs. Her percentage profit is

A. 11 1/9%

B. 20%

C. 25%

D. 80%

Show Answer

Answer: 25%

Explanation: Profit = 3000 − 2400 = 600. Percentage = (600 ÷ 2400) × 100 = 25%.

Question 7

A map is drawn to a scale of 1:200000. The actual distance, in km, of two towns 12.5 cm apart on the map is

A. 250

B. 25

C. 2.5

D. 0.25

Show Answer

Answer: 25

Explanation: 12.5 × 200000 = 2,500,000 cm = 25 km.

Question 8

In a school, the ratio of boys to girls is 4:5. If there are 180 girls, the total number of students is

A. 260

B. 280

C. 324

D. 405

Show Answer

Answer: 324

Explanation: 5 parts = 180 → 1 part = 36. Total parts = 9 → total = 9 × 36 = 324.

Question 9

The perimeter of a semicircle of radius 14 cm (π = 22/7) is

A. 36

B. 44

C. 58

D. 72

Show Answer

Answer: 72

Explanation: Perimeter = πr + 2r = (22/7×14) + 28 = 44 + 28 = 72.

Question 10

In the figure, O is the centre of a semicircular plate of internal radius 4 cm. Given PQ = 3 cm, the area of the shaded portion is

A. 5π/2

B. 6π

C. 33π/2

D. 33π

Show Answer

Answer: 33π/2

Explanation: Area = outer semicircle − inner semicircle using radii difference.

Question 11

A cubical tank of length 30 m and square base of area 25 m² is half full with water. The quantity of water in m³ is

A. 250

B. 375

C. 500

D. 750

Show Answer

Answer: 375

Explanation: Volume = base × height = 25 × 30 = 750 m³. Half full → 750 ÷ 2 = 375 m³.

Question 12

The area, in cm², of the shaded sector shown (radius 10 cm, angle 72°) is

A. 2π

B. 4π

C. 20π

D. 40π

Show Answer

Answer: 20π

Explanation: Area = θ/360 × πr² = 72/360 × π × 100 = 1/5 × 100π = 20π.

Question 13

The shaded portion in the Venn diagram represents

A. P ∩ Q

B. P ∩ Q'

C. Q − P

D. P − Q

Show Answer

Answer: Q − P

Explanation: Shaded region is inside Q but outside intersection → elements in Q only.

Question 14

If G represents girls and F represents football players, the statement “No girls play football” is written as

A. G ∩ F = ∅

B. G ∪ F = ∅

C. G ⊂ F

D. G ∩ F ≠ ∅

Show Answer

Answer: G ∩ F = ∅

Explanation: No common elements means intersection is empty set.

Question 15

The number of elements in sets P and Q are shown. Find x

A. 4

B. 2

C. 1

D. 0

Show Answer

Answer: 2

Explanation: Use total elements formula: n(P ∪ Q) = n(P) + n(Q) − n(P ∩ Q).

Question 16

The factors of a − 3b + 4ab − 12b² are

A. 4b (a − 3b)

B. (a − 3b)(1 − 4b)

C. (a − b)(12b − 3a)

D. (a − 3b)(1 + 4b)

Show Answer

Answer: (a − 3b)(1 + 4b)

Explanation: Factor by grouping: (a − 3b) + 4b(a − 3b) = (a − 3b)(1 + 4b).

Question 17

Simplify x²/(x² − 1) + x/(x − 1)

A. 1/(x+1)

B. x/(x+1)

C. (x+1)/x

D. x/(x−1)

Show Answer

Answer: x/(x+1)

Explanation: Factor denominator: x²−1 = (x−1)(x+1). Combine fractions and simplify.

Question 18

Given PV = kRT, express T in terms of P, V, k and R

A. PV/kR

B. PV/R

C. PR/kV

D. PV/k

Show Answer

Answer: PV/kR

Explanation: Rearranging: T = PV / (kR).

Question 19

x pens and y pencils cost 150 francs, and 2x pens and 3y pencils cost 375 francs. The cost of a pen is

A. 125

B. 100

C. 75

D. 25

Show Answer

Answer: 75

Explanation: Solve simultaneous equations → subtract first from second → find x.

Question 20

One solution of 2x² + 5x − 3 = 0 is

A. −3

B. 1/2

C. 3

D. −1/2

Show Answer

Answer: 1/2

Explanation: Solve quadratic: (2x−1)(x+3)=0 → x = 1/2 or −3.

Question 21

Given that (x + 2) is a factor of x² + 2x − 8, find k

A. 4

B. −2

C. −1

D. 2

Show Answer

Answer: −2

Explanation: Substitute x = −2 → expression = 0.

Question 22

The diagram represents the inequality

A. −1 < x ≤ 1

B. −1 ≤ x < 1

C. x ≥ 1

D. x ≤ −1

Show Answer

Answer: −1 < x ≤ 1

Explanation: Open circle at −1 (not included), closed at 1 (included).

Question 23

Given that 2^(x+1) = 16, find x

A. 2

B. 3

C. 4

D. 5

Show Answer

Answer: 3

Explanation: 16 = 2⁴ → x + 1 = 4 → x = 3.

Question 24

The second term of a sequence with sum Sn = 3n² − n + 5 is

A. 15

B. 8

C. 7½

D. 7

Show Answer

Answer: 8

Explanation: a₂ = S₂ − S₁ = (3×4−2+5) − (3×1−1+5) = 15 − 7 = 8.

Question 25

P varies inversely as square of q. If P = 3 when q = 2, find P when q = 1

A. 12

B. 6

C. 3/2

D. 1/4

Show Answer

Answer: 12

Explanation: P = k/q² → 3 = k/4 → k=12 → when q=1 → P=12.

Question 26

Find the value of p in the mapping diagram

A. 31

B. 9

C. 4

D. 3

Show Answer

Answer: 4

Explanation: Apply mapping rule f(x) = 2x + 5.

Question 27

The relation shown is described as

A. One-to-one

B. One-to-many

C. Many-to-one

D. Many-to-many

Show Answer

Answer: Many-to-many

Explanation: Multiple inputs map to multiple outputs.

Question 28

If f(x) = (x+6)/2, find f⁻¹(x)

A. 2/(x+6)

B. (x−6)/2

C. 2x−6

D. 2x+6

Show Answer

Answer: 2x−6

Explanation: Swap x,y: x = (y+6)/2 → y = 2x − 6.

Question 29

Given M is midpoint of PQ, find coordinates of Q

A. (7,2)

B. (2,2)

C. (5,2)

D. (−5,2)

Show Answer

Answer: (7,2)

Explanation: Use midpoint formula: M = (P+Q)/2 → solve for Q.

Question 30

Find the gradient of the line shown

A. 1

B. 2

C. 3

D. 4

Show Answer

Answer: 2

Explanation: Gradient = rise/run using graph coordinates.

Question 31

The equation of a straight line passing through (0,3) with gradient 2 is

A. y = 2x + 3

B. y = 3x + 2

C. y = 2x − 3

D. y = x + 3

Show Answer

Answer: y = 2x + 3

Explanation: Equation of line: y = mx + c. Here m = 2 and intercept c = 3.

Question 32

The distance between points (2,3) and (6,7) is

A. 4

B. 5

C. √32

D. √16

Show Answer

Answer: √32

Explanation: Distance = √[(6−2)² + (7−3)²] = √(16 + 16) = √32.

Question 33

Find the value of x if 3x − 5 = 10

A. 5

B. 3

C. 15

D. 2

Show Answer

Answer: 5

Explanation: 3x = 15 → x = 5.

Question 34

Solve x² − 4 = 0

A. x = 2

B. x = −2

C. x = ±2

D. x = 4

Show Answer

Answer: x = ±2

Explanation: x² = 4 → x = ±2.

Question 35

Simplify 5x − 2x + 3x

A. 6x

B. 5x

C. 3x

D. 10x

Show Answer

Answer: 6x

Explanation: Combine like terms: 5x − 2x + 3x = 6x.

Question 36

The next term in the sequence 3, 6, 12, 24, … is

A. 30

B. 36

C. 48

D. 60

Show Answer

Answer: 48

Explanation: Multiply by 2 each time → 24 × 2 = 48.

Question 37

The mean of 4, 6, 8, 10 is

A. 6

B. 7

C. 8

D. 9

Show Answer

Answer: 7

Explanation: Mean = (4+6+8+10)/4 = 28/4 = 7.

Question 38

The median of 1, 3, 5, 7, 9 is

A. 3

B. 5

C. 7

D. 9

Show Answer

Answer: 5

Explanation: Middle value = 5.

Question 39

The mode of 2, 2, 3, 4, 5 is

A. 2

B. 3

C. 4

D. 5

Show Answer

Answer: 2

Explanation: Most frequent value is 2.

Question 40

The probability of getting a head when tossing a fair coin is

A. 0

B. 1

C. 1/2

D. 2

Show Answer

Answer: 1/2

Explanation: 1 favourable outcome out of 2.

Question 41

The probability of rolling a 6 on a fair die is

A. 1/3

B. 1/6

C. 1/2

D. 1/4

Show Answer

Answer: 1/6

Explanation: One favourable outcome out of 6.

Question 42

If P(A) = 1/5, then P(not A) is

A. 4/5

B. 1/5

C. 5

D. 1

Show Answer

Answer: 4/5

Explanation: Complement = 1 − 1/5 = 4/5.

Question 43

The magnitude of vector (3,4) is

A. 5

B. 7

C. 4

D. 3

Show Answer

Answer: 5

Explanation: √(3² + 4²) = 5.

Question 44

The direction of vector (1,1) is

A. 45°

B. 90°

C. 180°

D. 270°

Show Answer

Answer: 45°

Explanation: Equal components → 45° direction.

Question 45

The order of a matrix with 2 rows and 3 columns is

A. 3 × 2

B. 2 × 3

C. 2 × 2

D. 3 × 3

Show Answer

Answer: 2 × 3

Explanation: Order = rows × columns.

Question 46

The transpose of a matrix is obtained by

A. Multiplying rows

B. Swapping rows and columns

C. Adding rows

D. Dividing columns

Show Answer

Answer: Swapping rows and columns

Explanation: Rows become columns.

Question 47

The range of 4, 6, 9, 3, 10 is

A. 6

B. 7

C. 10

D. 13

Show Answer

Answer: 7

Explanation: Range = max − min = 10 − 3 = 7.

Question 48

The median of 2, 5, 7, 9, 11 is

A. 5

B. 7

C. 9

D. 11

Show Answer

Answer: 7

Explanation: Middle value = 7.

Question 49

The mode of 1, 2, 2, 3, 4 is

A. 1

B. 2

C. 3

D. 4

Show Answer

Answer: 2

Explanation: Most frequent value = 2.

Question 50

The probability of not getting a head when tossing a coin is

A. 1

B. 0

C. 1/2

D. 2

Show Answer

Answer: 1/2

Explanation: Complement of getting head = 1 − 1/2 = 1/2.