Daily Practice · Higher Plus
October 1975 5-a-day
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The batch download puts all 5 tiers' October 1975 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1975In a vector proof you find that vector PQ = 6a - b and vector RS = 18a - 3b. What does this show about PQ and RS?
- 2nd October 1975A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 3rd October 1975A 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?
- 4th October 1975A car covers 350 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.
- 5th October 1975Simplify (x^2 + 5x - 24)/(x - 3).
- 6th October 1975y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 9.
- 7th October 1975A cuboid measures 4 cm by 6 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th October 1975A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th October 1975On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th October 1975Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 11th October 1975In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 12th October 1975A train slows steadily from 34 m/s to rest in 10 seconds. Work out its deceleration.
- 13th October 1975A cuboid measures 4 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th October 1975A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th October 1975A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 16th October 1975Simplify sqrt(45) + sqrt(245), giving your answer in the form a sqrt(b).
- 17th October 1975Make x the subject of 8x + 3 = y(x + 3).
- 18th October 1975y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 19th October 1975The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 20th October 1975A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 21st October 1975On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd October 1975A rectangle is 7 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd October 1975Write 3/(x + 5) + 7/(x - 1) as a single fraction.
- 24th October 1975y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 25th October 1975In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 26th October 1975The probability of winning a game is 1/4. A player expects 14 wins. How many games did they play?
- 27th October 1975A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 28th October 1975Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 29th October 1975Solve 6x^2 + 7x - 20 = 0.
- 30th October 1975y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 36.
- 31st October 1975In a vector proof you find that vector PQ = 4a - 5b and vector RS = 20a - 25b. What does this show about PQ and RS?