Daily Practice · Higher Plus
October 1971 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1971 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1971Rationalise the denominator of 77/sqrt(7), giving your answer in its simplest form.
- 2nd October 1971f(x) = 3x + 4 and g(x) = 3x - 4. Work out fg(5).
- 3rd October 1971y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 25.
- 4th October 1971A cuboid measures 4 cm by 7 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th October 1971A 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?
- 6th October 1971On 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?
- 7th October 1971Simplify sqrt(27) + sqrt(48), giving your answer in the form a sqrt(b).
- 8th October 1971The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 9th October 1971A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 10th October 1971The 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.
- 11th October 1971A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 12th October 1971A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 13th October 1971A rectangle is 10 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th October 1971A quadratic sequence starts 12, 25, 44, 69. Work out the second difference, and the coefficient of n^2.
- 15th October 1971y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 16th October 1971In 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.
- 17th October 1971The probability of winning a game is 1/4. A player expects 4 wins. How many games did they play?
- 18th October 1971On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th October 1971Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 20th October 1971Solve x^2 - 12x + 27 < 0.
- 21st October 1971y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 22nd October 1971In a vector proof you find that vector PQ = 3a + 5b and vector RS = 12a + 20b. What does this show about PQ and RS?
- 23rd October 1971A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 24th October 1971A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 25th October 1971A block has mass 430 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th October 1971Write x^2 - 14x - 13 in the form (x + a)^2 + b.
- 27th October 1971y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 81.
- 28th October 1971A cuboid measures 13 cm by 7 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th October 1971A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th October 1971On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st October 1971x = 188 and y = 60, each correct to the nearest whole number. Work out the upper bound of x - y.