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Recursos para tareas escolares en Nigeria

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Preguntas

Nigeria
23. Given that \( =x^{2}-3 x+9 \), find the value of \( \frac{d y}{d x} \) at \( (0,-3) \). (A) \( -\frac{1}{2} \) (B) \( -\frac{1}{4} \) (C) \( \frac{1}{4} \) (D) \( \frac{1}{2} \) 24. The mean of four numbers is 5 and the mean of another three numbers is 12 . Find the mean of seven numbers. (A) 10 (B) 9 (C) 8 (D) 7 25. Find the gradient of the normal to the curve \( =x^{3}-x^{2} \), at the point where \( x=2 \). (A) \( \frac{1}{8} \) (B) \( -\frac{1}{8} \) (C) 1 (D) \( -\frac{1}{24} \) 26. Which of the following is not an equation of a circle? (A) \( 3 x^{2}+3 y^{2}+5 x+7 y=5 \) (B) \( x^{2}+y^{2}- \) 27. Find the equation of the straight line that passes through \( (2,-5) \) and perpendicular to the line \( 3 x+2 y-4=0 \). (A) \( 3 y+2 x+5=0 \) (B) \( 3 y-2 x+15=0 \) (C) \( 3 y+2 x-19=0 \) 28. Calculate, correct to one decimal place, the length of the line joining points \( X(3,5) \) and \( (5,1) \). (A) 4.0 (D) \( 3 y-2 x+19=0 \) (B) 4.5 (C) 4.7 (D) 5.0 29. Find the unit vector in the direction of \( -5 i+12 j \). (A) \( \frac{1}{13}(-5 i-12 j) \) (B) \( \frac{1}{13}(5 i-12 j) \) (C) \( \frac{1}{13}(5 i+ \) 30. A curve is given by \( y=x^{2}-4 x-12 \). Find the axis of symmetry of the curve. (A) \( x=2 \) (B) \( y=2 \) (C) \( x=-2 \) (D) \( y=-2 \) 31. Find the coefficient of the 6 th term in the binomial expansion of \( \left(1-\frac{2 x}{3}\right)^{10} \) in ascending powers of \( x \) (A) \( -\frac{896 x^{6}}{9} \) (B) \( -\frac{896 x^{6}}{27} \) (C) \( -\frac{896 x^{5}}{27} \) (D) \( -\frac{896 x^{5}}{9} \) 32. The probabilities that Atta and Tunde will hit a target in a shooting contest are \( \frac{1}{6} \) and \( \frac{1}{9} \) respectively. Find the probability that only one of them will hit the target. (A) \( \frac{1}{54} \) (B) \( \frac{13}{54} \) (C) \( \frac{20}{27} \) (D) \( \frac{41}{54} \)
Cálculo Jan 22, 2025
13. A body of mass 42 kg increases its speed from \( 15 \mathrm{~m} / \mathrm{s} \) to \( 43 \mathrm{~m} / \mathrm{s} \) in 12 seconds. Find the force acting c the body. (A) 52 N (B) 98 N (C) 150 N (D) 203 N 14. Find the minimum value of \( =x^{2}+6 x-12 \). (A) -12 (B) -6 (C) -3 (D) -21 15. Given that \( y=2 x-1 \) and \( \Delta x=0.1 \), find \( \Delta y \). (A) 0.20 (B) 0.15 (C) 0.10 (D) 0.05 16. An exponential sequence (G.P.) is given by \( \frac{9}{2}, \frac{3}{4}, \frac{1}{8}, \ldots \ldots \). Find its sum to infinity. (A) \( 13 \frac{1}{2} \) (B) \( 4 \frac{1}{5} \) (C) \( € \) (D) \( 5 \frac{2}{5} \) 17. If \( r=i+2 j \) and \( =-I+3 j \), find \( |2 n-r| \). (A) 8.5 (B) 5.0 (C) 4.0 (D) 3.6 18. Find the area of a circle whose equation is \( { }^{2}+y^{2}-4 \cdot x+8 y+11=0 \). (A) \( 3 \pi \) (B) \( 9 \pi \) (C) \( \epsilon \) 19. Find the fourth term in the binomial expansion of \( (3 x-y)^{6} \). (A) \( -540 x^{3} y^{3} \) (B) \( -27 x^{3} \) (D) \( 12 \pi \) (C) \( 540 x^{4} y^{2} \) (D) \( -540 x^{4} y^{2} \) 20. Given that \( f(x)=x^{2}+3 x+1 \), find the value of \( x \) at the turning point. (A) 2 (B) \( 1 \frac{1}{2}(C \) (C) \( -1 \frac{1}{2} \) 21. In how many ways can 12 people be seated on a bench if only 5 spaces are available? (A) 950 2 (B) 11880 (C) 792 (D) 495 22. If \( K x^{2}-12 x+K=0 \) has equal roots, find the values of \( K \). \( (A)+2(B)+3 \) \( (C)+.6 \) (D) +9
Física Jan 22, 2025
1. If \( \frac{5}{\sqrt{2}}-\frac{\sqrt{8}}{8}=m \sqrt{2} \), find the value of \( m \). (A) \( \frac{12}{5} \) (B) \( \frac{9}{4} \) (C) \( \frac{7}{3} \) (D) \( \frac{5}{2} \) 2. Given that \( f: x \rightarrow \sqrt{x} \) and \( g: x \rightarrow 25-x^{2} \), find the value of \( \log (3) \). (A) 4 (B) 3 3. If \( \sqrt{x}-\frac{6}{\sqrt{x}}=1 \), find the value of \( x \). (A) 9 (B) 16 (C) 25 (D) 36 4. If \( 5 x+7=P(x+3)+Q(x-1) \), find the value of \( P \). (A) 3 (B) 2 (C) 1 (D) \( 0 \cdot\left(4 A^{\circ}\right)= \) 5. If \( y=x \sin x \), find \( \frac{d y}{d x} \). (A) \( \sin x-x \cos x \) (B) \( \sin x-\cos x \) (C) \( \sin x+x \cos x \) (D) \( \sin x+\cos x \) 6. A binary operation \( * \) is defined on the set of real numbers, \( R \) by \( * y=\frac{y^{2}-x^{2}}{2 x y}, x, y \neq 0 \), where \( x \) ar (A) \( \frac{13}{12} \) (B) \( \frac{5}{12} \) (C) \( -\frac{5}{12} \) (D) \( =\frac{13}{12} \) 7. Calculate the value of \( \lambda \) for which vectors \( (5 \lambda i+2 j) \) and \( (4 i-3 j) \) are perpendicular. (A) \( \frac{1}{2} \) (B) (C) \( \frac{10}{3} \) (D) \( \frac{3}{10} \) 8. If \( h(x)=x^{2}+p x+2 \) is divided by \( (x+3) \), the remainder is 5 , find \( p \). (A) 1 (B) 2 (C) 3 (D) 4 9. If the nth term of a linear sequence (A.P.) is \( (5 n-2) \), find the sum of the first 12 terms of \( t \) l sequence. (A) 120 (B) 183 (C) 366 (D) 732 10. Find the stationary point of the curve \( =3 x^{2}-2 x^{3} \). (A) \( (1,0) \) (B) \( (-1,0) \) (C) \( (1,1) \) (D) \( (-1,-1) \) 11. Solve: \( 2^{2 x}-5\left(2^{x}\right)+4=0 \) (A) \( x=0 \) and 1 (B) \( x=1 \) and 2 (C) \( x=0 \) and 2 (D) \( x=2 \) and 12. Express \( 75^{\circ} \) in radians leaving your answer in terms of \( \pi \). (A) \( \frac{3}{4} \pi \) (B) \( \frac{5}{6} \pi \) (C) \( \frac{5}{12} \pi \) (D) \( \frac{7}{6} \pi \) 13. A body of mass 42 kg increases its speed from \( 15 \mathrm{~m} / \mathrm{s} \) to \( 43 \mathrm{~m} / \mathrm{s} \) in 12 seconds. Find the force acting c the body. (A) 52 N (B) 98 N (C) 150 N (D) 203 N
Cálculo Jan 22, 2025
EXERCISE 5.1 1. Find the volume of the parallelopiped with adjacent sides. \[ \overline{O A}=3 \hat{i}-\hat{j}, \quad \overline{O B}=\hat{j}+2 \hat{k} \text {, and } \overline{O C}=\hat{i}+5 \hat{j}+4 \hat{k} \] extending from the origin of co-ordinates \( O \)
Geometría Jan 22, 2025
EXERCISE 5.1 1. Find the volume of the parallelopiped with adjacent sides. \[ \overline{O A}=3 \hat{i}-\hat{j}, \quad \overline{O B}=\hat{j}+2 \hat{k} \text {, and } \overline{O C}=\hat{i}+5 \hat{j}+4 \hat{k} \] extending from the origin of co-ordinates \( O \)
Geometría Jan 22, 2025
EXERCISE 5.1 1. Find the volume of the parallelopiped with adjacent sides. \[ \overline{O A}=3 \hat{i}-\hat{j}, \quad \overline{O B}=\hat{j}+2 \hat{k} \text {, and } \overline{O C}=\hat{i}+5 \hat{j}+4 \hat{k} \] extending from the origin of co-ordinates \( O \)
Geometría Jan 22, 2025
2. Find the volume of the tetrahedron whose vertices are the points \( A(2,-1,-3), B(4,1,3) \) \( C(3,2,-1) \) and \( D(1,4,2) \). Ans. \( 7 \frac{1}{3} \)
Geometría Jan 22, 2025
The equation of a line is \( y=5 x+2 \). Find the oquation of a line perpendiculat to it and passing through \( \left(4,-\frac{3)}{3}\right. \)
Geometría Jan 21, 2025
4 A line passos through \( (1,1) \) and \( (3,5) \). ind wein Ard the equation of a line perpendicular to this ine passing through \( (2,-1) \)
Geometría Jan 21, 2025
Aline passos through \( (1,1) \) and \( (3,5) \). Ard the the equation of 9 line perpendicular to this ine passing through \( (z,-1) \)
Geometría Jan 21, 2025
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