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Convert 72_{6} to a number in base three.

2211

2121

1212

1122

Convert 27_{10} to another number in base three.

1010_{3}

1100_{3}

1000_{3}

1001_{3}

Evaluate $\frac{1.25\times 0.025}{0.05}$, correct to 1 decimal place.

6.2

6.3

0.5

0.6

Calculate the time taken for N3,000 to earn N600 if invested at 8% simple interest.

3 years

$3\frac{1}{2}$ years

$1\frac{1}{2}$ years

$2\frac{1}{2}$ years.

Simplify $\frac{{3}^{-n}}{{9}^{1-n}}\times {27}^{n+1}$

3^{3}

3^{5}

3

3^{2}

If log 10_{4} = 0.6021, evaluate log_{10 }$4\frac{1}{2}$

0.9021

1.8063

0.2007

0.3011

Simplify $\frac{\sqrt{5}\left(\sqrt{147}-\sqrt{12}\right)}{\sqrt{15}}$

^{1}**/**_{5}

^{1}**/**_{9}

9

5

P, Q and R are subsets of the universal set U. The venn diagram showing the relationship* (P $\cap $ Q) $\cup $ R *is

.

.

.

.

If P =* { x : x is odd, -1 < x ≤ 20 } *and Q = *{ y : y is prime, -2 < y ≤ 25 }*, find P $\cap $ Q

{3,5,11,13,17,19}

{3,5,7,11,13,17,19}

{2,3,5,7,11,13,17,19}

{3,5,7,11,17,19}

If S = $\sqrt{{t}^{2}-4t+4}$, find *t* in terms of S.

S + 2

S – 2

S^{2} + 2

S^{2} – 2

if x – 4 is a factor of x^{2} – x – k, then k is

12

20

2

4

The remainder when 6p2 - p2 - 47p + 30 is divided by p – 3 is

42

63

18

21

P varies jointly as *m* and *u*, and varies inversely as *q*. Given that *p=4, m=3* and *u= 2* when *q = 1*, find the value of *p* when *m = 6*, *u = 4* and q = ^{3}*/*_{5}.

15

10

^{200}*/*_{5}

^{120}*/*_{5}

If *r* varies inversely as the square root of *s* and *t*, how does *s* vary with *r* and *t*?

s varies inversely as r^{2} and t.

s varies directly as r^{2} and t^{2} .

s varies directly as r and t.

s varies inversely as r and t^{2} .

The graph above is correctly represented by

y = x^{2} – 3x + 2

y = x^{2} – x – 1

y = x^{2} + x – 2

y = x^{2} – x – 2

Solve for x: **[x - 2] < 3**

−2 < x < 3

−1 < x < 5

x < 1

x < 5

The nth term of the progression $\frac{4}{2},\frac{7}{3},\frac{10}{4},\frac{13}{5}$... is

$\frac{3n+1}{n+1}$

$\frac{3n+1}{n-1}$

$\frac{3n-1}{n+1}$

$\frac{1-3n}{n+1}$

If a binary operation ∗ is defined by $x*y=x+2y$ , find **2 * (3 * 4)**

16

14

26

24

If $P=\left[\begin{array}{cc}5& 3\\ 2& 1\end{array}\right]$ and $Q=\left[\begin{array}{cc}4& 2\\ 3& 5\end{array}\right]$, find 2P + Q.

$\left[\begin{array}{cc}14& 8\\ 7& 7\end{array}\right]$

$\left[\begin{array}{cc}7& 7\\ 8& 14\end{array}\right]$

$\left[\begin{array}{cc}8& 14\\ 7& 7\end{array}\right]$

$\left[\begin{array}{cc}7& 7\\ 14& 8\end{array}\right]$

Find the inverse of $\left[\begin{array}{cc}5& 3\\ 6& 4\end{array}\right]$

$\left[\begin{array}{cc}2& -\frac{3}{2}\\ -3& \frac{5}{2}\end{array}\right]$

$\left[\begin{array}{cc}2& \frac{3}{2}\\ -3& -\frac{5}{2}\end{array}\right]$

$\left[\begin{array}{cc}2& \frac{3}{2}\\ -3& \frac{5}{2}\end{array}\right]$

$\left[\begin{array}{cc}2& -\frac{3}{2}\\ -3& -\frac{5}{2}\end{array}\right]$

In the diagram above, find the value of x.

40º

45º

15º

30º

The value of x in the figure above is

100º

70º

130º

110º

If the angles of a quadrilateral are (3y + 10)º , (2y + 30)º , (y + 20)º and 4yº , find the value of y.

42º

66º

12º

30º

A square tile has side 30cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?

576

720

336

420

Find the length of a chord which subtends an angle 90º at the centre whose radius is 8cm.

$8\sqrt{2}$cm

$8\sqrt{3}$cm

4 cm

8 cm

A chord of a circle subtends an angle 120º at the centre of a circle of diameter $4\sqrt{3}$cm. Calculate the area of the major sector.

16π cm^{2}

32π cm^{2}

4π cm^{2}

8π cm^{2}

If the mid-point of the line PQ is (2, 3) and the point P is (−2, 1), find the coordinate of the point Q.

(6, 3)

(8, 6)

(5, 6)

(0, 4)

In triangle PQR, q = 8 cm, r = 6 cm and cos P =$\frac{1}{12}$ . Calculate the value of p.

10 cm

$\sqrt{108}$cm

9 cm

$\sqrt{92}$cm

If tanθ = $\frac{3}{4}$, find the value of sin θ + cos θ.

$1\frac{2}{5}$

$1\frac{1}{3}$

$1\frac{2}{3}$

$1\frac{3}{5}$

If y = (2x + 2)^{3} , find $\frac{dy}{dx}$

6(2x + 2)

3(2x + 2)

6(2x + 2)^{2}

3(2x + 2)^{2}

If y = x sin x, find $\frac{dy}{dx}$

cos x – x sin x

cos x + x sin x

sin x + x sin x

sin x – cos x.

The radius of a circle is increasing at the rate of 0.02 cms^{-1} . Find the rate at which the area is increasing when the radius of the circle is 7cm.

0.53 cm^{-2}s^{-1}

0.35 cm^{-2}s^{-1}

0.88 cm^{-2}s^{-1}

0.75 cm^{-2}s^{-1}

Integrate $\left(\frac{1+x}{{x}^{3}}\right)dx$

${x}^{2}-\frac{1}{x}+k$

$2{x}^{2}-\frac{1}{x}+k$

$-\frac{1}{2{x}^{2}}-\frac{1}{x}+k$

$-\frac{{x}^{2}}{2}-\frac{1}{x}+k$

Evaluate ${\int}_{0}^{\frac{\mathrm{\pi}}{2}}\mathrm{sin}xdx$

−1

−2

2

1

The bar chart above shows the allotment of time (in minutes) per week for selected subjects in a certain school. What is the total time allocated to the six subjects per week?

720 mins.

960 mins.

200 mins.

460 mins.

The pie chart above shows the statistical distribution of 80 students in five subjects in an examination. Calculate how many students offer Mathematics.

40

50

12

30

Age | 20 | 25 | 30 | 35 | 40 | 45 |

No. of people | 3 | 5 | 1 | 1 | 2 | 3 |

Calculate the median age of the frequency distribution in the table above.

30

35

20

25

If the variance of 3 + x, 6, 4, x and 7 – x is 4 and the mean is 5, find the standard deviation.

2

3

$\sqrt{2}$

$\sqrt{3}$

Score | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Freq. | 1 | 0 | 7 | 5 | 2 | 3 | 1 | 1 |

The table above shows the scores of 20 students in Further Mathematics test. What is the range of the distribution?

6

3

10

7

$\frac{5!}{2!2!}$

$\frac{5!}{2!3!}$

$\frac{5!}{2!}$

$\frac{5!}{3!}$

In how many ways can 3 seats be occupied if 5 people are willing to sit?

20

5

120

60

What is the probability that an integer x (1 ≤ x ≤ 25) chosen at random is divisible by both 2 and 3?

$\frac{1}{5}$

$\frac{1}{25}$

$\frac{3}{4}$

$\frac{1}{25}$

A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor an orange.

$\frac{1}{8}$

$\frac{7}{24}$

$\frac{2}{3}$

$\frac{3}{8}$