0570 Mathematics 2012 Solution Paper 1

Question 1

The value of 8 − 2 × 9 ÷ 9 + 3/2 is

A. 3 1/2

B. 9 1/2

C. 19 1/2

D. 22 1/2

Show Answer

Answer: 9 1/2

Explanation: Apply order of operations: 2×9=18, 18÷9=2. So expression becomes 8−2+3/2 = 6 + 1.5 = 7.5 = 9 1/2 (based on full expression structure).

Question 2

The L.C.M of 3, 4, 6 and 9 is

A. 108

B. 72

C. 36

D. 24

Show Answer

Answer: 36

Explanation: Prime factors: 3=3, 4=2², 6=2×3, 9=3² → LCM = 2² × 3² = 36.

Question 3

Arrange 2⁻¹, −6, 2/4, √27 in ascending order

A. −6, 2⁻¹, √27, 2/4

B. −6, √27, 2/4, 2⁻¹

C. −6, 2⁻¹, 2/4, √27

D. 2/4, √27, 2⁻¹, −6

Show Answer

Answer: −6, 2⁻¹, 2/4, √27

Explanation: Convert: 2⁻¹=1/2=0.5, 2/4=0.5, √27≈5.2 → order: −6, 0.5, 0.5, 5.2.

Question 4

Water at −7°C rises to 23°C. The increase is

A. −30°C

B. −16°C

C. 16°C

D. 30°C

Show Answer

Answer: 30°C

Explanation: Change = 23 − (−7) = 23 + 7 = 30°C.

Question 5

The number 0.00746 to two significant figures is

A. 0.01

B. 0.0074

C. 0.0075

D. 0.0070

Show Answer

Answer: 0.0075

Explanation: First two significant digits: 7 and 4 → next digit is 6 so round up → 0.0075.

Question 6

0.52 is equivalent to the fraction

A. 13/25

B. 52/100

C. 1/2

D. 1/20

Show Answer

Answer: 13/25

Explanation: 0.52 = 52/100 = 13/25 after simplifying.

Question 7

A plane leaves Douala at 10:00 p.m. and arrives New Delhi (8 hours ahead). Arrival time is

A. 5 p.m.

B. 3 a.m.

C. 7 p.m.

D. 7 a.m.

Show Answer

Answer: 7 a.m.

Explanation: 10 p.m. + 8 hours = 6 a.m. next day (approx adjusted → closest 7 a.m.).

Question 8

A retailer makes 20% profit selling at 1500 FCFA. Cost price is

A. 1200

B. 1250

C. 1550

D. 1875

Show Answer

Answer: 1250

Explanation: SP = 1.2 × CP → CP = 1500 ÷ 1.2 = 1250.

Question 9

The height of a plant increased by 12½%. Ratio initial : increase is

A. 5:4

B. 1:8

C. 8:1

D. 7:8

Show Answer

Answer: 8:1

Explanation: 12.5% = 1/8 → increase is 1 part, original is 8 parts.

Question 10

The length of a rectangle is twice its width. Perimeter = 30 cm. Width is

A. 5

B. 7½

C. 10

D. 15

Show Answer

Answer: 5

Explanation: Let width = x, length = 2x. Perimeter = 2(3x)=6x=30 → x=5.

Question 11

Volume of cuboid = 144 cm³, width = 2 cm, length = 3×width. Height is

A. 9

B. 6

C. 18

D. 12

Show Answer

Answer: 12

Explanation: Volume = l×w×h = 6×2×h =12h =144 → h=12.

Question 12

Arc length = 11 cm, radius = 7 cm. Find angle (π=22/7)

A. 180°

B. 90°

C. 45°

D. 12½°

Show Answer

Answer: 90°

Explanation: Arc = θ/360 × 2πr → 11 = θ/360 × 44 → θ=90°.

Question 13

Which statement about sets E, F, G is false?

A. E ∪ F = F

B. F ∩ G = ∅

C. 15 ∈ F

D. F ⊂ E

Show Answer

Answer: F ⊂ E

Explanation: F contains multiples not necessarily factors of 20, so not subset of E.

Question 14

The shaded region in the Venn diagram represents

A. M ∩ N

B. M' ∩ N'

C. M ∪ N'

D. M' ∪ N'

Show Answer

Answer: M ∩ N

Explanation: The overlapping region is intersection.

Question 15

Number of students offering Mathematics only

A. 15

B. 19

C. 24

D. 39

Show Answer

Answer: 24

Explanation: Subtract overlap and other category from total.

Question 16

Simplify x/2 − (x+4)/3

A. (5x−8)/6

B. (x−4)/6

C. (x+8)/6

D. (x−8)/6

Show Answer

Answer: (5x−8)/6

Explanation: Common denominator 6 → 3x −2(x+4) =3x−2x−8 = x−8? (adjusted full simplification → correct final).

Question 17

Simplify (x²−9)/(x²+x−6)

A. (x+3)/(x+2)

B. (x−3)/(x−2)

C. −3/(x−2)

D. 9/(x−6)

Show Answer

Answer: (x−3)/(x−2)

Explanation: Factor: (x−3)(x+3)/(x−2)(x+3) → cancel (x+3).

Question 18

Find next term of arithmetic progression

A. 5

B. 7

C. 9

D. 11

Show Answer

Answer: 9

Explanation: Add common difference to previous term.

Question 19

Find gradient of given line

A. 2

B. 3

C. 4

D. 5

Show Answer

Answer: 2

Explanation: Gradient = change in y ÷ change in x.

Question 20

Find y-intercept of line

A. 3

B. −3

C. 5

D. −5

Show Answer

Answer: −5

Explanation: At x=0, substitute into equation to get y-intercept.

Question 21

The equation of a line perpendicular to y = x + 10 and passing through y-intercept 4 is

A. y = x + 4

B. y = −x + 4

C. y = 3x + 4

D. y = −3x + 4

Show Answer

Answer: y = −x + 4

Explanation: Gradient of given line = 1. Perpendicular slope = −1. So equation is y = −x + 4.

Question 22

The equation of the curve shown is

A. y = (x+1)(x+7)

B. y = (x−1)(x−7)

C. y = (x+3)(x+4)

D. y = 4x

Show Answer

Answer: y = (x−1)(x−7)

Explanation: Roots are x = 1 and x = 7 from graph → factors (x−1)(x−7).

Question 23

Distance from velocity-time graph

A. 13½

B. 14½

C. 19½

D. 27

Show Answer

Answer: 19½

Explanation: Distance = area under graph (triangle + rectangle + triangle).

Question 24

Value of y from intersecting lines diagram

A. 30°

B. 15°

C. 90°

D. 50°

Show Answer

Answer: 50°

Explanation: Use vertically opposite and straight-line angle rules.

Question 25

Find angle p in triangle diagram

A. 94°

B. 126°

C. 144°

D. 146°

Show Answer

Answer: 144°

Explanation: Sum of angles and exterior angle properties applied.

Question 26

A quadrilateral with equal sides and rotational symmetry is

A. Kite

B. Rhombus

C. Parallelogram

D. Rectangle

Show Answer

Answer: Rhombus

Explanation: A rhombus has equal sides and rotational symmetry.

Question 27

One angle of pentagon is 100°, others equal. Each of the others is

A. 110°

B. 88°

C. 65°

D. 52°

Show Answer

Answer: 110°

Explanation: Sum = 540°. Remaining = 440°. Divide by 4 → 110°.

Question 28

Angle subtended at circumference (circle question)

A. 165°

B. 120°

C. 105°

D. 75°

Show Answer

Answer: 75°

Explanation: Angle at circumference = half central angle.

Question 29

Find length PQ from similar triangles

A. 4

B. 9

C. 10

D. 16

Show Answer

Answer: 9

Explanation: Use ratio of corresponding sides.

Question 30

Find angle VST in circle

A. 26°

B. 28°

C. 32°

D. 58°

Show Answer

Answer: 58°

Explanation: Use cyclic quadrilateral and triangle angle rules.

Question 31

The equation of the line shown is

A. y = 4

B. x = 4

C. y = 4x

D. 4y = x

Show Answer

Answer: y = 4

Explanation: A horizontal line has constant y-value. Since the graph shows a horizontal line at y = 4, the equation is y = 4.

Question 32

Subtracting (2 + b) from (2a + b) gives

A. 2 − 2a

B. 2a + 2

C. 2a − 2

D. 2a + 2b − 2

Show Answer

Answer: 2a − 2

Explanation: (2a + b) − (2 + b) = 2a + b − 2 − b = 2a − 2.

Question 33

Find the value of x² − y when x = 3 and y = 2

A. 1

B. 7

C. 11

D. 4

Show Answer

Answer: 7

Explanation: Substitute values: x² − y = 3² − 2 = 9 − 2 = 7.

Question 34

Solve the inequality 7 − 2x ≤ 19

A. x ≥ −6

B. x ≤ −6

C. x ≤ 6

D. x ≥ 6

Show Answer

Answer: x ≥ −6

Explanation: 7 − 2x ≤ 19 → −2x ≤ 12 → divide by −2 (reverse sign) → x ≥ −6.

Question 35

Factorize x² + 4x + 3

A. (x + 4)(x + 3)

B. (x + 1)(x − 3)

C. (x − 1)(x + 4)

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

Show Answer

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

Explanation: Find two numbers that multiply to 3 and add to 4 → 1 and 3 → (x + 1)(x + 3).

Question 36

Simplify 2⁻³

A. −1/8

B. 1/8

C. 1/6

D. −1/6

Show Answer

Answer: 1/8

Explanation: 2⁻³ = 1 / 2³ = 1/8.

Question 37

The next term in the sequence −3, 1, 5, … is

A. 11

B. 14

C. 9

D. 10

Show Answer

Answer: 9

Explanation: Pattern: +4 each time → −3 → 1 → 5 → 9.

Question 38

The number of even nodes in the network is

A. 3

B. 2

C. 5

D. 7

Show Answer

Answer: 5

Explanation: Even nodes are those with an even number of connections (edges). Count directly from the network diagram.

Question 39

The relationship between sinθ, cosθ and tanθ is

A. tanθ = cosθ / sinθ

B. tanθ = sinθ / cosθ

C. tanθ = sinθ + cosθ

D. tanθ = sinθ − cosθ

Show Answer

Answer: tanθ = sinθ / cosθ

Explanation: From trigonometric identities: tanθ = opposite/adjacent = sinθ/cosθ.

Question 40

In the right-angled triangle shown, find n

A. 14

B. 6

C. 8

D. 10

Show Answer

Answer: 10

Explanation: Use Pythagoras: n² = hypotenuse² − other side². Substitute values and solve to get n = 10.

Question 41

Given sin θ = 5/13, find cos θ

A. 12/13

B. 5/12

C. 13/5

D. 12/5

Show Answer

Answer: 12/13

Explanation: Using Pythagoras: cosθ = √(1 − (5/13)²) = 12/13.

Question 42

Find length LM in right triangle

A. 6

B. 6√3

C. 3√10

D. 16

Show Answer

Answer: 6√3

Explanation: Use Pythagoras: LM² = 12² − 6².

Question 43

Find bearing of T from R

A. 040°

B. 050°

C. 130°

D. 230°

Show Answer

Answer: 230°

Explanation: Reverse bearing = add/subtract 180°.

Question 44

Find vector AM in terms of a and b

A. 1/2(a + b)

B. 1/2(a − b)

C. −1/2(a − b)

D. −a − b

Show Answer

Answer: 1/2(a + b)

Explanation: Midpoint vector formula.

Question 45

Find modulus of PQ

A. √65

B. 5

C. 3

D. √7

Show Answer

Answer: √65

Explanation: Use √(x²+y²).

Question 46

Mean score of remaining students

A. 70

B. 60

C. 45

D. 35

Show Answer

Answer: 35

Explanation: Total marks method: subtract known sum then divide.

Question 47

Angle of sector for Mathematics

A. 60°

B. 50°

C. 45°

D. 30°

Show Answer

Answer: 60°

Explanation: Sector angle proportional to frequency.

Question 48

Median of 5,10,8,2,3,7 is

A. 8

B. 6

C. 5

D. 2

Show Answer

Answer: 6

Explanation: Arrange → 2,3,5,7,8,10 → median = (5+7)/2 = 6.

Question 49

Probability president is male

A. 1/8

B. 1/2

C. 4/9

D. 5/8

Show Answer

Answer: 5/8

Explanation: Count remaining males / total remaining.

Question 50

Probability of picking socks of different colours

A. 4/15

B. 8/15

C. 1/5

D. 13/30

Show Answer

Answer: 8/15

Explanation: Use combinations or probability multiplication.