Daily Practice · Higher Plus
August 1991 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1991y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 2nd August 1991In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 3rd August 1991The probability of winning a game is 3/8. A player expects 42 wins. How many games did they play?
- 4th August 1991A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 5th August 1991A block has mass 340 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th August 1991The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 7th August 1991y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 25.
- 8th August 1991In a vector proof you find that vector PQ = 2a - 2b and vector RS = 8a - 8b. What does this show about PQ and RS?
- 9th August 1991A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 10th August 1991On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 11th August 1991x = 167 and y = 149, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th August 1991A quadratic sequence starts 1, 5, 13, 25. Work out the second difference, and the coefficient of n^2.
- 13th August 1991A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 14th August 1991A cuboid measures 12 cm by 5 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th August 1991A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th August 1991A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 17th August 1991A car covers 120 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th August 1991Solve x^2 + 3x - 4 < 0.
- 19th August 1991y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 20th August 1991A cuboid measures 11 cm by 11 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st August 1991A bag holds 5 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd August 1991On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd August 1991Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.
- 24th August 1991Write x^2 - 16x - 4 in the form (x + a)^2 + b.
- 25th August 1991y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 26th August 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.
- 27th August 1991A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 28th August 1991A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 29th August 1991Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 30th August 1991Work out the coordinates of the turning point of y = x^2 - 8x - 5.
- 31st August 1991y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 4.