Daily Practice · Higher Plus
April 1991 5-a-day
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The batch download puts all 5 tiers' April 1991 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1991A block has mass 620 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd April 1991Work out the nth term of the quadratic sequence 9, 14, 23, 36, ...
- 3rd April 1991y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 4th April 1991In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 5th April 1991The probability of winning a game is 1/10. A player expects 3 wins. How many games did they play?
- 6th April 1991A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 7th April 1991x = 88 and y = 65, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th April 1991The point (-3, 2) lies on y = f(x). Write down its image on y = f(x + 5).
- 9th April 1991y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 49.
- 10th April 1991In a vector proof you find that vector PQ = 3a + 4b and vector RS = 15a + 20b. What does this show about PQ and RS?
- 11th April 1991A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 12th April 1991On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th April 1991A car covers 840 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th April 1991Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 15th April 1991A train slows steadily from 14 m/s to rest in 8 seconds. Work out its deceleration.
- 16th April 1991A cuboid measures 4 cm by 5 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th April 1991A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th April 1991A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 19th April 1991Rationalise the denominator of 30/sqrt(3), giving your answer in its simplest form.
- 20th April 1991f(x) = 3x + 9 and g(x) = 5x + 8. Work out fg(-1).
- 21st April 1991y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 22nd April 1991A cuboid measures 7 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd April 1991A bag holds 7 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th April 1991On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th April 1991Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 26th April 1991The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 27th April 1991y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 28th April 1991The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 29th April 1991A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.
- 30th April 1991A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?