Tests and Challenges

Correct, 0.00798516 to three significant figures.

Simplify: (11_two)².

Solve: 2^{√(2x + 1)} = 32.

If log₁₀2 = m and log₁₀3 = n, find log₁₀24 in terms of m and n.

Find the 5th term of the sequence: 2, 5, 10, 17,….

If P = (-3 < x < 1} and q = {-1 < x <3), where x is a real number, find P n Q.

Factorize 6pq – 3rs -3ps +  6qr.

What number should be subtracted from the sum of and     to give

Mensah is 5 years old and Joyce is thrice as old as Mensah. In how many years will Joyce be twice as old as Mensah?

If 16 x 2^(X+1) = 4^x x 81^(1-x), find the value of x.

The circumference of a circular track is 9 km. A cyclist rides round it a 2 number of times and stops after covering a distance of 302 km. How far is the cyclist from the starting point.

Simplify: 2√7 – 14/√7  + 7/√21

If 4x + 2y = 16 and 6x – 2y = 4, find the value of (y-x).

Given that R is directly proportional to L and inversely proportional to P, R = 3 when L = 9 and P=0.8, find R when L = 15 and P= 1.8.

In The diagram, LABC and LBCD are right angles, LBAD = 1 and LEDF=70°. Find the value of t°.

The sum of the interior angles of a regular polygon with k sides is (3k-10) right angles. Find the size of the exterior angle.

Make U the subject of the relation

A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of ₦22,800.00 was paid as import duty, calculate the cost of the engine.

The height of an equilateral triangle is 10√3 cm Calculate its perimeter.

In  LMN, |LM| = 6 cm, LLMN = 90°, LLNM = x° and sinx = 3/2. Find the area of     LMN. A. 60 cm²

Consider the statements: P: All students offering Literature (L) also offer History (H); Q: Students offering History (H) do not offer Geography (G). Which of the Venn diagrams correctly illustrate the two statement?

Find the quadratic equation whose roots are -2q and Sq.

If tanɵ = 3/4, 180° <  ɵ < 270°, find the value of cos ɵ

If

Find p?

The diagonals of a rhombus are 12 cm and 5 cm. Calculate its perimeter

In the diagram,     XYZ is produced to T. If |XY| = |ZY| and LXYT = 40°, find ZXZT

A solid brass cube is melted and re-cast as a solid cone of height and base radius r. If the height of the cube is h, find in terms of h

Which of the following is not an exterior angle of a regular polygon?

From a point , a man moves 12 km due West and them moves 12 km due South to another point Q. Calculate the bearing of T from Q.

In the diagram, O is the centre of circle PORS, LPOR = 72° and OR/IPS. Find LOPS.

A trapezium of sides 10 cm and 21 cm and height 8 cm is inscribed in a circle of radius 7 cm. Calculate the area of the region not covered by the trapezium. (Take Л = 22/7)

Find, correct to two decimal places, the mean of 3/2, 8/3, 15/4, 24/5 and 25/6

A cyclist moved at a speed of X km/h for 2 hours. He then increased his speed by 2 km/h for the next 3 hours. If the total distance covered is 36 km, calculate his initial speed, X

Find the value of (x + y) in the diagram

In the diagram, MP is a tangent to the circle NOR, LPNQ = 60° and RQ = RN). Find the angle marked r

Find the first quartile of 7, 8, 7, 9, 11, 8, 7, 9, 6 and 8.

In the diagram, PQRS is a circle Find the value of x

A cone has a base radius of 8 cm and height 11 cm Calculate, correct to two decimal places, the curved surface area (Take π = 22/7)

Given that sin x = 3/5,  0° ≤ x ≤ 90° evaluate (tan y + 2 cos x)

In the diagram. EC is a diameter of the circle ABCDE IF LABC =158. find LADE.

The table shows the height of thirty seven players of a basketball team Calculate, correct to one decimal place, the mean height of the players.

XT/ is a line segment with the coordinates X(-1.-12) and Y(p, q) If the midpoint of XY is (-1, -2), find the coordinates of Y

Five hundred tickets were sold for a concert Tickets for adults and children were sold at $4.50 and $3.00 respectively if the total receipts for the concert was $1.987 50 how many tickets for adults were sold?

The distance (d) between two villages is more than 18 km but not more than 23 km. Which of these inequalities represents the statement?

The pie chart represents the distribution of fruits on display in a shop. If there are 60 apples on display, how many oranges are there?

A box contains 40 identical balls of which 10 are red and 12 are blue. If a ball is selected at random from the box, what is the probability that it is neither red nor blue?

A fair die is tossed twice. What is the probability of getting a sum of at least 10?

A mam will be (x + 10) years old in 8years time. If 2 years ago he was 63 years, find the value of x.

The equation of a line is given as 3x – 5y – 7. Find its gradient (slope).

For what value of x is 4 – 2x/x + 1 undefined?