Daily Practice · Higher Plus
October 1991 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1991In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 2nd October 1991The probability of winning a game is 3/5. A player expects 18 wins. How many games did they play?
- 3rd October 1991A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 4th October 1991Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 5th October 1991f(x) = 5x + 2. Work out the inverse function f^-1(x).
- 6th October 1991y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 7th October 1991In a vector proof you find that vector PQ = 2a - 3b and vector RS = 10a - 15b. What does this show about PQ and RS?
- 8th October 1991A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 9th October 1991On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th October 1991Simplify sqrt(75) + sqrt(27), giving your answer in the form a sqrt(b).
- 11th October 1991Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 12th October 1991y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 13th October 1991A cuboid measures 3 cm by 10 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th October 1991A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th October 1991A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 16th October 1991A rectangle is 15 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th October 1991Use the iteration x(n+1) = cube root of (8x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
- 18th October 1991y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
- 19th October 1991A cuboid measures 9 cm by 13 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th October 1991A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st October 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?
- 22nd October 1991Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 23rd October 1991Work out the nth term of the quadratic sequence 11, 24, 43, 68, ...
- 24th October 1991A train slows steadily from 24 m/s to rest in 4 seconds. Work out its deceleration.
- 25th October 1991The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 26th October 1991A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 27th October 1991A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 28th October 1991A block has mass 750 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th October 1991The point (4, -6) lies on y = f(x). Write down its image on y = f(x) - 1.
- 30th October 1991y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 31st October 1991In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.