NECO · 2023 · SSCE · General Maths · Paper 2

1. (i)

   the relationship between $P$, $Q$ and $Z$ ($P$ in terms of $Q$ and $Z$);

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2. (ii)

   $Z$ when $P = 3$ and $Q = 5$.

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1. (a)

   The sum of the interior angles of a regular polygon is $1440^\circ$. (i) How many sides has the polygon? (ii) Find the size of each exterior angle.

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   Separate values with commas, e.g. 3, −2
2. (b)

   Find the principal that will earn ₦29,880.00 in 15 years at $3\%$ per annum simple interest.

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1. (a)

   Find (i) the value of $\theta$; (ii) the radius of the circle.

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   Separate values with commas, e.g. 3, −2
2. (b)(i)

   Calculate the area of the shaded region, correct to three significant figures. $\left[\pi = \frac{22}{7}\right]$

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3. (b)(ii)

   What type of triangle is $\triangle AOB$?

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   Equilateral

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1. (a)

   Solve the equation $27^{2x - 1} \times \left(\frac13\right)^{-(3x + 2)} = 9^{x + 3}$.

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2. (b)

   Differentiate $(2x^2 + 5)^4$ with respect to $x$.

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1. (a)

   Draw a pie chart to illustrate this information. (Enter the sector angles for English, Mathematics, Physics, French and Biology.)

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2. (b)

   If two teachers are chosen to represent the school at a workshop, what is the probability that both come from Physics or both from Biology?

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1. (a)

   If $135_k = 231_{\text{four}}$, find the value of $k$.

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2. (b)

   A sector of a circle of radius $21\text{ cm}$ has an angle of $120^\circ$ at the centre. Calculate its (i) perimeter; (ii) area. $\left[\pi = \frac{22}{7}\right]$

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   Separate values with commas, e.g. 3, −2
3. (c)

   Simplify $\dfrac{3}{\sqrt5 + \sqrt2} - \dfrac{1}{\sqrt5 - \sqrt2}$, leaving your answer in surd form.

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1. (a)

   The sum of the ages of a man and his daughter is 60 years. Six years ago, the man's age was three times that of his daughter. Find their present ages (man, daughter).

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   Separate values with commas, e.g. 3, −2
2. (b)

   Find the equation whose roots are $-\frac34$ and $\frac56$.

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   $24x^2 - 2x - 15 = 0$

3. (c)

   Evaluate $4\left(1 - \dfrac{144}{169}\right)^{\frac12} \times \left(\dfrac{2}{13}\right)^{-1}$.

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1. (a)

   Evaluate without using tables $5\log2 + \log40 - \log12.8$.

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2. (b)

   Find the equation of the curve which passes through $(-2, 5)$ and has gradient $6x^2 + 8x - 3$ at any point.

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3. (c)

   Differentiate $y = 3x^2 + 4x - 5$ with respect to $x$.

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1. (a)

   Given $A = \begin{pmatrix} 3 & 2 & -1 \\ 1 & 0 & 1 \\ 2 & -2 & 0 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & 2 & -3 \\ 3 & -1 & 1 \\ 0 & -2 & 2 \end{pmatrix}$, evaluate (i) $3A - 2B$; (ii) $|3A - 2B|$.

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2. (b)

   Mr. Tony took a loan of ₦120,000.00 at $12\%$ per annum compound interest to buy a piece of land. (i) If he paid the loan in three years, what was the total amount paid? (ii) Find his profit if he later sold the land for ₦350,000.00 without any additional expenses.

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   Separate values with commas, e.g. 3, −2

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1. (a)

   Depth of water (cm)

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1. (a)

   Construct a triangle $ABC$ such that $|AB| = 5\text{ cm}$, $|AC| = 7\text{ cm}$ and $\angle BAC = 120^\circ$.

   Model answer

   Use only a ruler and a pair of compasses: leave every construction arc visible, because the examiner looks for them. Draw $AC = 7$ cm. At $A$, construct $120^\circ$ (two $60^\circ$ steps along the same arc from $AC$). Mark $B$ on that arm with $AB = 5$ cm and join $BC$.

2. (b)

   Construct (i) the locus $l_1$ of points equidistant from $A$ and $C$; (ii) the locus $l_2$ of points $4.5\text{ cm}$ from $C$.

   Model answer

   (i) Points equidistant from $A$ and $C$ lie on the perpendicular bisector of $AC$: with a radius more than half of $AC$, draw arcs from $A$ and from $C$ that cross above and below the line, and join the crossings. (ii) Points $4.5$ cm from $C$ lie on the circle centre $C$, radius $4.5$ cm.

3. (c)

   Locate the points of intersection, $N_1$ and $N_2$, of $l_1$ and $l_2$.

   Model answer

   $N_1$ and $N_2$ are where the perpendicular bisector cuts the circle. By calculation they are $2\sqrt{4.5^2 - 3.5^2}$ apart, so $|N_1N_2| \approx$ 5.7 cm, and $|BC| = \sqrt{109} \approx 10.4$ cm.

4. (d)

   Measure (i) $|N_1N_2|$; (ii) $|BC|$ (cm).

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   Separate values with commas, e.g. 3, −2

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1. (a)

   value of $2x$;

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2. (b)

   mean deviation;

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3. (c)

   standard deviation, correct to two decimal places.

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