Find the turning point on the curve y = x2 – 2x

1. Find the turning point on the curve y = x2 – 2x (0 mk)

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Find the focus and directrix of the parabola; y2 – 4y – 12 + 16 = 0

1. Find the focus and directrix of the parabola; y² – 4y – 12 + 16 = 0 (0 mk)

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Find the number of arrangements that can be formed using the letters of the words (a) EQUATION (b) TUMBAKU.

1. Find the number of arrangements that can be formed using the letters of the word EQUATION. (0 mk)
2. Find the number of arrangements that can be formed using the letters of the word TUMBAKU. (0 mk)

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Suppose the items processed on a certain machine are found to be 1% defective. Determine the probability of obtaining 4 defectives in a random sample batch of 80 such items

1. Suppose the items processed on a certain machine are found to be 1% defective. Determine the probability of obtaining 4 defectives in a random sample batch of 80 such items. (0 mk)

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You are given the following figure. Prove that ΔXYZ is congruent to ΔXAZ.

1. You are given the following figure. Prove that ΔXYZ is congruent to ΔXAZ. (0 mk)

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Outline any four qualities of a well stated specific objective in Mathematics lesson plan.

1. Outline any four qualities of a well stated specific objective in Mathematics lesson plan. (0 mk)

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Evaluate

1. Evaluate (0 mk)

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Find the equation of an ellipse with foci

1. Find the equation of an ellipse with foci (0 mk)

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define the following terms as used in Mathematics lesson: (a) Mathematics logbook. (b) Lesson plan. (c) Scheme of work.

1. define the following terms as used in Mathematics lesson: (a) Mathematics logbook. (0 mk)
2. define the following terms as used in Mathematics lesson: (b) Lesson plan. (0 mk)
3. define the following terms as used in Mathematics lesson: (c) Scheme of work. (0 mk)

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Prove that the vector area of a quadrilateral ABCD with diagonals AC and BD is given by ½ |AC x BD|

1. Prove that the vector area of a quadrilateral ABCD with diagonals AC and BD is given by ½ |AC x BD| (0 mk)

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The roots of a polynomial equation 2x³ – 5x² + 7x – 8 = 0 are α, β and γ. Find the equation whose roots are: (i) α – 1, β – 1 and γ – 1 (b) The roots of the equation x² + 2px + q = 0 differs by 2, show that p² = 1 + q

1. The roots of a polynomial equation 2x³ – 5x² + 7x – 8 = 0 are α, β and γ. Find the equation whose roots are α – 1, β – 1 and γ – 1. (0 mk)
2. Find the equation whose roots are α – 1, β – 1 and γ – 1 (0 mk)
3. The roots of the equation x² + 2px + q = 0 differs by 2, show that p² = 1 + q (0 mk)
4. The roots of the equation x² + 2px + q = 0 differs by 2, show that p² = 1 + q (0 mk)

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There two types of fertilizers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil nutrient composition, a farmer found that she needs at least 14kg of nitrogen and 14kg of phosphoric acid for her crop. If F1 costs 600 Tsh. Per kilogram (kg) and F2 costs 500 Tsh. per kilogram. (a) determine how much of each type of fertilizer should be used so that the nutrient requirements are met at minimum cost; (b) state the minimum cost.

1. determine how much of each type of fertilizer should be used so that the nutrient requirements are met at minimum cost (0 mk)
2. state the minimum cost. (0 mk)

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(a) Use standard results of to find the sum of the first 50 terms of the series 2 + 6 + ... + (n² – n) (b) Prove that 2b² = 9ac where a,b and c are real numbers, given that one root of the quadratic equation ax² + bx + c = 0 is twice the other. (c) Find an equation with integral coefficients whose roots are the cubes of the roots of the equation 2x² + 5x – 6 = 0

1. Use standard results of to find the sum of the first 50 terms of the series 2 + 6 + ... + (n² – n) (0 mk)
2. Prove that 2b² = 9ac where a,b and c are real numbers, given that one root of the quadratic equation ax² + bx + c = 0 is twice the other. (0 mk)
3. Find an equation with integral coefficients whose roots are the cubes of the roots of the equation 2x² + 5x – 6 = 0 (0 mk)

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explain the following components of a lesson plan as used in the teaching and learning of Mathematics: (a) Preliminary information (b) Objectives (c) Lesson development (d) Students’ and teachers’ evaluation.

1. Preliminary information (0 mk)
2. Objectives (0 mk)
3. Lesson development (0 mk)
4. Students’ and teachers’ evaluation. (0 mk)

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