Core Mathematics — 2000

Express \(\frac{7}{19}\) as a percentage, correct to one decimal place

Express 398753 correct to three significant figures

simplify \(\frac{10}{\sqrt{32}}\)

Find the missing number in the addition of the following numbers, in base seven \(\begin{matrix} 4 & 3 & 2 & 1\\ 1 & 2 & 3 & 4\\ * & * & * & *\\ 1&2&3&4&1 \end{matrix}\)

What fraction must be subtracted from the sum of \(2\frac{1}{6}\) and \(2\frac{7}{12}\) to give \(3\frac{1}{4}\)?

Simplify \(\left(\frac{16}{81}\right)^{-\frac{3}{4}}\times \sqrt{\frac{100}{81}}\)

Which of the following numbers is perfect cube?

If \(104_x = 68\), find the value of x

The ages of three men are in the ratio 3:4:5. If the difference between the ages of the oldest and youngest is 18 years, find the sum of the ages of the three men

Given that \(log_4 x = -3\), find x.

Given that the logarithm of a number is \(\bar{1}.8732\), find, correct to 2 significant figures the square root of the number.

A car moves at an average speed of 30kmh\(^{-1}\), how long does it take to cover 200 meters?

A man bought a television set on hire purchase for N25,000, out of which he paid N10,000, if he is allowed to pay the balance in eight equal installments, find the value of each installment.

A tree is 8km due south of a building. Kofi is standing 8km west of the tree. How far is Kofi from the building?

A tree is 8km due south of a building. Kofi is standing 8km west of the tree. Find the bearing of Kofi from the building

Which of the following bearings is equivalent to S50°W?

In the diagram, AB is a vertical pole and BC is horizontal. If |AC| = 10m and |BC| = 5m, calculate the angle of depression of C from A

The bar chart shows the distribution of marks scored by a group of students in a test. Use the chart to answer the question below How many students scored 4 marks and above?

The bar chart shows the distribution of marks scored by a group of students in a test. Use the chart to answer the question below How many students took the test?

Calculate the standard deviation of the following marks; 2, 3, 6, 2, 5, 0, 4, 2

The probabilities that Kodjo and Adoga pass an examination are \(\frac{3}{4}\) and \(\frac{3}{5}\) respectively. Find the probability of both boys failing the examination

Which of the following statement is not true about a rectangle? I.Each diagonal cuts the rectangle into two congruent triangles. II. A rectangle has four lines of symmetry III. The diagonals intersect at right angles

In the diagram, PQRS is a circle center O. PQR is a diameter and ∠PRQ = 40°. Calculate ∠QSR.

Each side of a regular convex polygon subtends an angle of 30° at its center. Calculate each interior angle

If the interior angles of hexagon are 107°, 2x°, 150°, 95°, (2x-15)° and 123°, find x.

In the diagram, POS and ROT are straight lines, OPQR is a parallelogram. |OS| = |OT| and ∠OST = 50°. Calculate ∠OPQ.

Given that x = -\(\frac{1}{2}\) and  y = 4 evaluate 3x\(^2y+xy^2\)

Given that \(27^{(1+x)}=9,)\ find x

If x varies inversely as y and \(x = \frac{2}{3}\) when y = 9, find the value of y when \(x=\frac{3}{4}\)

Given that (2x + 7) is a factor of \(2x^2 + 3x - 14\), find the other factor

Simplify \(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\)

Form an inequality for a distance d meters which is more than 18m, but not more than 23m

Find the equation whose roots are -8 and 5

Make t the subject of formula \(k = m\sqrt{\frac{t-p}{r}}\)

Solve the equation \(3y^2\) = 27y

Find the value of x such that the expression \(\frac{1}{x}+\frac{4}{3x}-\frac{5}{6x}+1\) equals zero

Given that p varies directly as q while q varies inversely as r, which of the following statements is true?

In the diagram, PQS is a circle with center O. RST is a tangent at S and ∠SOP = 96o. Find ∠PST

A bicycle wheel of radius 42cm is rolled over a distance 66 meters. How many revolutions does it make?[Take \(\pi = \frac{22}{7}\)]

The height of a pyramid on square base is 15cm. if the volume is 80cm^3, find the area of the square base.

A tap leaks at the rate of 2cm\(^3\) per seconds. How long will it take the tap to fill a container of 45 liters capacity? (1 liters = 1000cm\(^3\))

The length of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm\(^2\), find the perpendicular distance between the parallel sides

The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\pi = \frac{22}{7}\)

In the diagram, |PQ| = |PS| Which of the following statements is true?

The area of a circle is 38.5cm2. Find its diameter [take \(\pi = \frac{22}{7}\)]

Find the volume (in cm\(^3\)) of the solid shown above

Solve the equation 3 + 5x - 2x\(^2\) = 0

If the simple interest on N2000 after 9 months is N60, at what rate per annum is the interest charged?