Daily Practice · Higher Plus
September 1975 5-a-day
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The batch download puts all 5 tiers' September 1975 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1975In a vector proof you find that vector PQ = a + 4b and vector RS = 2a + 8b. What does this show about PQ and RS?
- 2nd September 1975A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 3rd September 1975On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th September 1975Simplify sqrt(45) + sqrt(45), giving your answer in the form a sqrt(b).
- 5th September 1975The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 6th September 1975y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 7th September 1975A cuboid measures 8 cm by 5 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th September 1975A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th September 1975A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 10th September 1975A rectangle is 30 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th September 1975A quadratic sequence starts 6, 19, 42, 75. Work out the second difference, and the coefficient of n^2.
- 12th September 1975y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 64.
- 13th September 1975A cuboid measures 12 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th September 1975A bag holds 3 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th September 1975On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th September 1975Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).
- 17th September 1975Solve x^2 + x - 2 < 0.
- 18th September 1975A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 19th September 1975The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 20th September 1975A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 21st September 1975A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 22nd September 1975A block has mass 640 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd September 1975Write x^2 - 16x - 7 in the form (x + a)^2 + b.
- 24th September 1975y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 25th September 1975In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 26th September 1975The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 27th September 1975On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th September 1975x = 107 and y = 79, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th September 1975Work out the coordinates of the turning point of y = x^2 + 4x + 3.
- 30th September 1975y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.