Core Mathematics 2020 - WASSCE

WASSCE CORE MATHEMATICS

Question 1

Evaluate, correct to two decimal places, 75.0785 - 34.624 + 9.83.

Question 2

If X = {x:x < 7} and Y = {y:y is a factor of 24} are subsets of µ = {1, 2, 3, ......, 10}, find X ∩ Y.

Question 3

Simplify: \[\left[\left(\frac{16}{9}\right)^{-\frac{3}{2}} \times 16^{-\frac{3}{4}}\right]^{\frac{1}{3}}\]

Question 4

Find the least value of x which satisfies the equation 4x = 7 (mod 9)

Question 5

Express 1 + 2 log₁₀3 in the form log₁₀q

Question 6

If \(101_2 + 12_y = 23_5\), find the value of y.

Question 7

An amount of ₦ 550,000.00 was realized when a principal, x was saved at 2% simple interest for 5 years. Find the value of x.

Question 8

Given that (√3 + √5)/√5 = x + y√15, find the value of (x + y)

Question 9

If x = 3 and y = -1, evaluate 2(x² - y³).

Question 10

Solve 3x - 2y = 10 and x + 3y = 7.

Question 11

The implication x ⇒ y is equivalent to

Question 12

The first of a Geometric Progression (G.P) is 3 and the 5th term is 48. Find the common ratio.

Question 13

Solve: (1/3)(5 - 3x) < (2/5)(3 - 7x).

Question 14

Make m the subject of the relation k = √((m - y)/(m + 1)).

Question 15

Find the quadratic equation whose roots are \(\frac{1}{2}\) and \(-\frac{1}{3}\).

Question 16

Given that x is directly proportional to y and inversely proportional to z, x = 15 when y = 10 and z = 4, find the equation connecting x, y and z.

Question 17

Two buses start from the same station at 9.00 am and travel in opposite directions along the same straight road. The first bus travels at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240 km apart?

Question 18

A solid cuboid has length 7 cm, width 5 cm and height 4 cm. Calculate its total surface area.

Question 19

**DIAGRAM WILL BE PROVIDED** In the diagram, PQ//SR. Find the value of x.

Question 20

Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3).

Question 21

The expresson \(\frac{5x + 3}{6x(x + 1)}\) will be undefined when x equals

Question 22

A man is five times as old as his son. In four years time, the product of their ages would be 340. If the son's age is y, express the product of their ages in terms of y.

Question 23

Simplify: a/b - b/a - c/b.

Question 24

**DIAGRAM WILL BE PROVIDED** In the diagram, XZY is an equilateral triangle of side 6 cm and T is the midpoint of XY. Find tan (∠ XZT).

Question 25

A fence 2.4 m tall, is 10 m away from a tree of height 16 m. Calculate the angle of elevation of the top of the tree from the top of the fence.

Question 26

Fati buys milk at ₦ x per tin and sells each at a profit of ₦ y. If she sells 10 tins of milk, how much does she receive from the sales?

Question 27

If tan y is positive and sin y is negative, in which quadrant would y lie?

Question 28

The dimensions of a rectangular base of a right pyramid are 9 cm by 5 cm. If the volume of the pyramid iis 105 cm3, how high is the pyramid?

Question 29

Each interior angle of a regular polygon is 168°. Find the number of sides of the polygon.

Question 30

**DIAGRAM WILL BE PROVIDED** In the diagram, MN//PQ, ∠ MNP = 2x and ∠ NPQ = (3x - 50°). Find the value of ∠ NPQ.

Question 31

The length of an arc of a circle of radius 3.5 cm is \(1\frac{19}{36}\) cm. Calculate, correct to the nearest degree, the angle subtended by the arc at the centre of the circle. [Take π = \(\frac{22}{7}\)]

Question 32

**DIAGRAM WILL BE PROVIDED** In the diagram, PU//SR, PS//TR, QS//UR. |UR| = 15 cm, |SR| = 8 cm, |PS| = 10 cm and area of ∆SUR = 24 cm2. Calculate the area of PTRS.

Question 33

**DIAGRAM WILL BE PROVIDED** In the diagram, PQR is a circle with centre O. If ∠ OPQ = 48°, find the value of m.

Question 34

**DIAGRAM WILL BE PROVIDED** The pie chart shows the population of men, women and children in a city. If the population of the city is 1,800,000, how many men are there?

Question 35

The mean of the numbers 15, 21, 17, 26, 18 and 29 is 21. Calculate the standard deviation.

Question 36

**DIAGRAM WILL BE PROVIDED** In the diagram, O is the centre of the circle. SOQ is a diameter and ∠ SRP = 37°. Find ∠ PSQ.

Question 37

A box contains 12 identical balls, of which 5 are red, 4 blue and the rest are green. Use this information to answer the question below If a ball is selected at random from the box, what is the probability that it is green?

Question 38

A box contains 12 identical balls, of which 5 are red, 4 blue and the rest are green. Use this information to answer the question below If two balls are selected at random one after the other with replacement, what is the probability that both are red?

Question 39

**DIAGRAM WILL BE PROVIDED** In the diagram, PQ is a straight line. If m = \(\frac{1}{2}(x + y + z)\), find the value of m.

Question 40

**TABLE WILL BE PROVIDED** The points on a linear graph are as shown in the table. Find the gradient (slope) of the line.

Question 41

**DIAGRAM WILL BE PROVIDED** In the diagram, O is the centre of the circle, PQ and RS are tangents to the circle. Find the value of (m + n).

Question 42

**DIAGRAM WILL BE PROVIDED** In the diagram, O is the centre of the circle. If ∠ NLM = 74°, ∠ LMN = 39° and ∠ LOM = x, find the value of x.

Question 43

Which of the following is not a sufficient condition for two triangles to be congruent?

Question 44

A woman received a discount of 20% on a piece of cloth she purchased from a shop. If she paid USD 525.00, what was the original price?

Question 45

The interquartile range of a distribution is 7. If the 25th percentile is 16, find the upper quartile.

Question 46

**DIAGRAM WILL BE PROVIDED** The graphs of the equations y = 2x + 5 and y = 2x² + x - 1 are shown. Use the information to answer the question below Find the points of intersection of the two graphs.

Question 47

**DIAGRAM WILL BE PROVIDED** The graphs of the equations y = 2x + 5 and y = 2x² + x - 1 are shown. Use the information to answer the question below If x = -2.5, what is the value of y on the curve?

Question 48

If (x + 2) is a factor of x² + px - 10, find the value of p.