Daily Practice · Higher Plus
October 1970 5-a-day
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The batch download puts all 5 tiers' October 1970 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1970In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 3 in terms of an integer n?
- 2nd October 1970y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 3rd October 1970A cuboid measures 4 cm by 4 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th October 1970A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th October 1970A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 6th October 1970Expand and simplify (9 + sqrt(6))(9 - sqrt(6)).
- 7th October 1970Make x the subject of 4x + 4 = y(x + 4).
- 8th October 1970y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 81.
- 9th October 1970A cuboid measures 14 cm by 4 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th October 1970A bag holds 5 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th October 1970On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th October 1970A block has mass 730 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th October 1970Write 4/(x - 1) + 6/(x - 5) as a single fraction.
- 14th October 1970A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 15th October 1970The 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.
- 16th October 1970A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 17th October 1970A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 18th October 1970x = 114 and y = 38, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th October 1970Solve 8x^2 + 6x - 9 = 0.
- 20th October 1970y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 21st October 1970In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 22nd October 1970The probability of winning a game is 1/5. A player expects 2 wins. How many games did they play?
- 23rd October 1970On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th October 1970A car covers 620 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th October 1970f(x) = 6x + 12. Work out the inverse function f^-1(x).
- 26th October 1970y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 27th October 1970In a vector proof you find that vector PQ = 3a + 2b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 28th October 1970A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 29th October 1970A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 30th October 1970Rationalise the denominator of 36/sqrt(3), giving your answer in its simplest form.
- 31st October 1970Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.