Questions in mathematics

Questions in mathematics

📝 Answered - By rounding to one significant figure, estimate the answers to these questions: a) $59 \div 25$ b) $\frac{682}{71}$ c) $\frac{91 \times 18}{58}$

📝 Answered - Select the best answer for the question. What is $6^2$ in expanded form? A. 12 B. 36 C. $2 \times 2 \times 2 \times 2 \times 2 \times 2$ D. $6 \times 6$

📝 Answered - Given the function [tex]f(x)=4|x-5|+3[/tex], for what values of [tex]x[/tex] is [tex]f(x)=15[/tex]? A. [tex]x=2, x=8[/tex] B. [tex]x=1.5, x=8[/tex] C. [tex]x=2, x=7.5[/tex] D. [tex]x=0.5, x=7.5[/tex]

📝 Answered - An equation has solutions of m = –5 and m = 9. Which could be the equation? A. (m + 5)(m – 9) = 0 B. (m – 5)(m + 9) = 0 C. m² – 5m + 9 = 0 D. m² + 5m – 9 = 0

📝 Answered - Evaluate the limit as x approaches 0 of the expression [tex]\( \frac{\cos x \sin^2 x - 1 + \cos^2 x}{2x^4} \)[/tex].

📝 Answered - Section B (5 marks) Instructions: Each of the following mathematical statements is either true or false. If the statement is true or false, write the question number on your answer sheet and write TRUE if the statement is true or FALSE if the statement is false. 1. The region in a circle bounded by two radii and an arc is a sector. 2. A cylinder has a base area of 75 cm² and height of 10 cm. The quantity of water when the cylinder is half full is 375 cm³. 3. Two points P(1, -1) and Q(5, 7) are on a straight line. Given that M is the midpoint of PQ, then the coordinates of M are (-2, -4). 4. Given the equation of the lines L₁: 2x + y = 8 and L₂: 6y - mx = 3, the value of m when L₁ and L₂ are perpendicular is -3. 5. Two angles α and θ are such that α + θ = 90°. The angles α and θ are complementary. Section C (10 marks). Show all steps in your working. Exercise 1 The functions f and g are defined as f: x → 2x + 3, g: x → mx - 2, where x ∈ R, the set of real numbers and m is a constant. Find: a) f(-5/2) (1 mark) b) f⁻¹(13) (1 mark) c) fg(x) in terms of m (1 mark) d) The value of m for which fg(x) = gf(x) (1 mark) Exercise 2 Mr. Ngede shares a certain amount of money among his three children Azoh, Che, and Ngong. Two-fifths of the money was given to Che, one-half of the remainder to Azoh, and the balance of 150,000 FCFA to Ngong. PROBLEM (15 MARKS) Show all the steps in your working. Sixty students were asked to harvest oranges in a school farm. The number of oranges harvested per student was recorded in the frequency distribution table below: | Number of oranges harvested | Number of students | |-----------------------------|--------------------| | 3 - 5 | 1 | | 6 | 4 | | 7 | 1 | | 8 | 2 | | 9 | 1 | | 10 | 2 | | 12 | 13 | | 13 | 2 | i) State the mode (1 mark) ii) Find the mean number of oranges harvested to one decimal place (4 marks) iii) Calculate the median (3 marks) iv) Draw a grouped frequency table for the classes: 3 - 5, 6 - 8, 9 - 11, and 12 - 14 (4 marks) v) Represent the grouped data on a histogram (2 marks) vii) Repeat is chosen at random. Find the probability that the student picked 13 oranges (2 marks) Find the fraction of the money given to: a) Both Azoh and Ngong b) Ngong c) Calculate the amount: i. That was shared ii. Given to Azoh iii. Given to Che e) Find the percentage of the amount given to Azoh

📝 Answered - What is the equation of the line that is perpendicular to the given line and has an $x$-intercept of 6? $y=-\frac{3}{4} x+8$ $y=-\frac{3}{4} x+6$ $y=\frac{4}{3} x-8$ $y=\frac{4}{3} x-6

📝 Answered - Motivate learners. 3.1. Cardinal, ordinal, and nominal numbers are the three basic types of numbers; understanding them is crucial for developing a strong foundation in mathematics, particularly for learners in the Intermediate Phase. 3.1.1. Define the three basic types of numbers mentioned above using your own understanding.

📝 Answered - Evaluate: [tex]\begin{array}{c} \sum_{n=1}^4 3(7)^{n-1} \\ S=[?]\\ \end{array}[/tex] Remember: for a geometric series, [tex]S=\frac{a\left(1-r^n\right)}{1-r}[/tex]

📝 Answered - What is a combination of operations on letters and numbers? A. factor B. variable C. term D. expression