Daily Practice · Higher Plus
October 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1959 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1959A cuboid measures 3 cm by 4 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd October 1959A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd October 1959A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 4th October 1959x = 119 and y = 55, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th October 1959The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 6th October 1959y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 7th October 1959A cuboid measures 12 cm by 14 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th October 1959A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th October 1959On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th October 1959A car covers 240 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th October 1959A quadratic sequence starts 5, 20, 43, 74. Work out the second difference, and the coefficient of n^2.
- 12th October 1959y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 13th October 1959The 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.
- 14th October 1959A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 15th October 1959A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 16th October 1959Rationalise the denominator of 10/sqrt(2), giving your answer in its simplest form.
- 17th October 1959Solve x^2 + 5x - 6 > 0.
- 18th October 1959y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
- 19th October 1959In 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.
- 20th October 1959The probability of winning a game is 7/10. A player expects 63 wins. How many games did they play?
- 21st October 1959On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd October 1959Simplify sqrt(80) + sqrt(45), giving your answer in the form a sqrt(b).
- 23rd October 1959Write x^2 - 6x - 1 in the form (x + a)^2 + b.
- 24th October 1959A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.
- 25th October 1959In a vector proof you find that vector PQ = 3a + 2b and vector RS = 9a + 6b. What does this show about PQ and RS?
- 26th October 1959A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 27th October 1959A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 28th October 1959A rectangle is 13 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th October 1959Work out the coordinates of the turning point of y = x^2 - 2x + 12.
- 30th October 1959y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 31st October 1959A cuboid measures 3 cm by 8 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.