NOVDEC FIRST SERIES -
CORE-MATHEMATICS TRIAL QUESTIONS
1. Three candidates K, L and M were voted into office as school prefects. K secured 45% of the votes, L had 33% of the votes and M had the rest of the votes. If M secured 1,430 votes, Calculate,
a) The total number of votes cast;
b) How many more votes K received than
2: a) Using ruler and a pair of compasses only, construct triangle ABC in which │AB│ = 8cm, │BC│= 9cm and angle ABC = 75o
b) Measure angle BAC
3(a) Kofi bought six books and ten pencils from a store. Ama bought three books and twenty-two pencils of the same kind from that store. If each of them paid Ȼ17,000.00 for the items, find the cost of
i. each pencil
ii. each book
iii. two books and four pencils
(b) Find the truth set of 3x + 8/x = 10, x 0
4: A boy 1.5 m tall is standing 12 m away from a church building which has a tower on top of its roof. The top of the cross on the tower is 14.6 m away from the boy’s head(eyes). If the boy has to raise his eyes through an angle of 31° in order to see the top of the roof, calculate,
a) correct to the nearest degree, the angle through which the boy must raise his eyes to see the top of the cross on the tower.
b) correct to one decimal place, the height of the top of the cross from ground:
c) correct to one decimal place the height of the church building.
5: (a) Using a scale of 2 cm to 2 units on both axes, draw on a graph sheet two perpendicular axes OX and OY for the intervals -10 ≤ x ≤ 10 and -10 ≤ y ≤ 10
(b) Draw,, labeling all vertices and indicating the coordinates clearly,
i) ΔPQR with coordinates P(2, 0), Q(8, -4) and R (8, 0);
ii) the image ΔP1Q1R1 of ΔPQR under a reflection in the line y = 2 where P→P1, Q→Q1 and R→R1
iii) the image ΔP2Q2R2 of ΔPQR under a rotation through 90o about the origin, where P→P2, Q→Q2 and R→R2
iv) the image ΔP3Q3R3 of ΔPQR under a rotation through 180o about the origin, where P→P3, Q→Q3 and R→R3
(c) What single transformation maps ΔP3Q3R3 on ΔP2Q2R2 ?
6. a) If x5 = 1024 find the value of x
b) Given that log107 = 0.8451 and log103 = 0.47771, find without using calculator log10 (9/7)
find without
7: a) (3.46)2 - (1.54)2 = 10x, find the value of x.
b) Find the truth set of the equation 5x2 = (x+2)(x+3)
Solution
(3.46)² - (1.54)² = 10x
(3.46+1.54) (3.46-1.54) = 10x
5.00 (1.92) = 10x
x = = 0.96
b)
5x² = (x+2)(x+3) = x²+5x+6
4x²-5x-6=0
4x²-8x+3x-6=0
4x(x-2)+3(x-2) = 0
(4x+3)(x-2) = 0
4x+3=0 or x-2 = 0
x=-¾ or x = 2
{x:x= -¾, 2}
8: a) A chord PQ of a circle of radius 5 cm subtends an angle of 70° at the centre, O. Find correct to 3 significant figures,
i. the length of the chord PQ;
ii. the length of the arc PQ;
iii. the area of the sector POQ;
iv. the area of the minor segment cut off by PQ.
b) A right circus cone has base radius 5 cm and height 12 cm. Calculate
i. its volume;
ii. its total surface area
9: a) Solve the equation 42x × 16x+1 = 64
b) R varies inversely as the cube of S. If R = 9 when S = 3 , find S when R = 243/64
10: a) Copy and complete the following tables for values of the relation y = 4 + 5x -2x2 for – 3 ≤ x ≤ 5
b) Using 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 4 + 5x – 2x2 for -3 ≤ x ≤ 5
c) From your graph, find the
i. value of x for which y is maximum
ii. gradient at x = 0
iii. values of x for which 1+ 5x - 2x2 = 0
X -3 -2 -1 0 1 2 3 4 5
y -14 4 7 -21
10: a) Draw a table of multiplication ⊗ in modulo 8 on the set (2,3,5,7)
b) Use your table to find the solution set of
i. 3 ⊗ n = 5
ii. n ⊗ n = 1
c) The set P =(-2, -1, 0, 1, 2) maps onto Q by the function f(x) = x2 – 2, where x ∈ P.
i. Find the elements of Q
ii. Draw a diagram showing the mapping between P and Q.
Papers for NOVDEC First series Registration will be available dito dito 💯💯
Kindly join this channel if you have registered ‼️‼️‼️✅
CORE-MATHEMATICS TRIAL QUESTIONS
1. Three candidates K, L and M were voted into office as school prefects. K secured 45% of the votes, L had 33% of the votes and M had the rest of the votes. If M secured 1,430 votes, Calculate,
a) The total number of votes cast;
b) How many more votes K received than
2: a) Using ruler and a pair of compasses only, construct triangle ABC in which │AB│ = 8cm, │BC│= 9cm and angle ABC = 75o
b) Measure angle BAC
3(a) Kofi bought six books and ten pencils from a store. Ama bought three books and twenty-two pencils of the same kind from that store. If each of them paid Ȼ17,000.00 for the items, find the cost of
i. each pencil
ii. each book
iii. two books and four pencils
(b) Find the truth set of 3x + 8/x = 10, x 0
4: A boy 1.5 m tall is standing 12 m away from a church building which has a tower on top of its roof. The top of the cross on the tower is 14.6 m away from the boy’s head(eyes). If the boy has to raise his eyes through an angle of 31° in order to see the top of the roof, calculate,
a) correct to the nearest degree, the angle through which the boy must raise his eyes to see the top of the cross on the tower.
b) correct to one decimal place, the height of the top of the cross from ground:
c) correct to one decimal place the height of the church building.
5: (a) Using a scale of 2 cm to 2 units on both axes, draw on a graph sheet two perpendicular axes OX and OY for the intervals -10 ≤ x ≤ 10 and -10 ≤ y ≤ 10
(b) Draw,, labeling all vertices and indicating the coordinates clearly,
i) ΔPQR with coordinates P(2, 0), Q(8, -4) and R (8, 0);
ii) the image ΔP1Q1R1 of ΔPQR under a reflection in the line y = 2 where P→P1, Q→Q1 and R→R1
iii) the image ΔP2Q2R2 of ΔPQR under a rotation through 90o about the origin, where P→P2, Q→Q2 and R→R2
iv) the image ΔP3Q3R3 of ΔPQR under a rotation through 180o about the origin, where P→P3, Q→Q3 and R→R3
(c) What single transformation maps ΔP3Q3R3 on ΔP2Q2R2 ?
6. a) If x5 = 1024 find the value of x
b) Given that log107 = 0.8451 and log103 = 0.47771, find without using calculator log10 (9/7)
find without
7: a) (3.46)2 - (1.54)2 = 10x, find the value of x.
b) Find the truth set of the equation 5x2 = (x+2)(x+3)
Solution
(3.46)² - (1.54)² = 10x
(3.46+1.54) (3.46-1.54) = 10x
5.00 (1.92) = 10x
x = = 0.96
b)
5x² = (x+2)(x+3) = x²+5x+6
4x²-5x-6=0
4x²-8x+3x-6=0
4x(x-2)+3(x-2) = 0
(4x+3)(x-2) = 0
4x+3=0 or x-2 = 0
x=-¾ or x = 2
{x:x= -¾, 2}
8: a) A chord PQ of a circle of radius 5 cm subtends an angle of 70° at the centre, O. Find correct to 3 significant figures,
i. the length of the chord PQ;
ii. the length of the arc PQ;
iii. the area of the sector POQ;
iv. the area of the minor segment cut off by PQ.
b) A right circus cone has base radius 5 cm and height 12 cm. Calculate
i. its volume;
ii. its total surface area
9: a) Solve the equation 42x × 16x+1 = 64
b) R varies inversely as the cube of S. If R = 9 when S = 3 , find S when R = 243/64
10: a) Copy and complete the following tables for values of the relation y = 4 + 5x -2x2 for – 3 ≤ x ≤ 5
b) Using 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = 4 + 5x – 2x2 for -3 ≤ x ≤ 5
c) From your graph, find the
i. value of x for which y is maximum
ii. gradient at x = 0
iii. values of x for which 1+ 5x - 2x2 = 0
X -3 -2 -1 0 1 2 3 4 5
y -14 4 7 -21
10: a) Draw a table of multiplication ⊗ in modulo 8 on the set (2,3,5,7)
b) Use your table to find the solution set of
i. 3 ⊗ n = 5
ii. n ⊗ n = 1
c) The set P =(-2, -1, 0, 1, 2) maps onto Q by the function f(x) = x2 – 2, where x ∈ P.
i. Find the elements of Q
ii. Draw a diagram showing the mapping between P and Q.
Papers for NOVDEC First series Registration will be available dito dito 💯💯
Kindly join this channel if you have registered ‼️‼️‼️✅
