Daily Practice · Higher Plus
September 1970 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1970 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1970A quadratic sequence starts 15, 27, 43, 63. Work out the second difference, and the coefficient of n^2.
- 2nd September 1970y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 3rd September 1970A cuboid measures 14 cm by 10 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th September 1970A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th September 1970On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th September 1970x = 41 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th September 1970Solve x^2 + 6x > 0.
- 8th September 1970y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 9th September 1970A cuboid measures 7 cm by 9 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th September 1970A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th September 1970A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 12th September 1970A car covers 830 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th September 1970Write x^2 - 4x - 10 in the form (x + a)^2 + b.
- 14th September 1970y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 16.
- 15th September 1970The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 16th September 1970A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 17th September 1970On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th September 1970Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 19th September 1970Work out the coordinates of the turning point of y = x^2 + 8x + 1.
- 20th September 1970A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 21st September 1970In 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.
- 22nd September 1970The probability of winning a game is 1/5. A player expects 10 wins. How many games did they play?
- 23rd September 1970A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 24th September 1970Simplify sqrt(50) + sqrt(98), giving your answer in the form a sqrt(b).
- 25th September 1970Simplify (x^2 - x - 6)/(x + 2).
- 26th September 1970y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 27th September 1970In a vector proof you find that vector PQ = 4a - 4b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 28th September 1970A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 29th September 1970On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th September 1970A rectangle is 4 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.