Daily Practice · Higher Plus
January 1971 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1971 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1971A cuboid measures 13 cm by 9 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd January 1971A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd January 1971On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 4th January 1971A block has mass 480 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th January 1971Simplify (x^2 - 12x + 32)/(x - 4).
- 6th January 1971y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 7th January 1971A cuboid measures 6 cm by 13 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th January 1971A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th January 1971A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 10th January 1971x = 70 and y = 12, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th January 1971In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 12th January 1971y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 81.
- 13th January 1971The 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.
- 14th January 1971A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 15th January 1971On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th January 1971A car covers 260 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th January 1971Make x the subject of 7x + 8 = y(x + 8).
- 18th January 1971A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 19th January 1971In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 20th January 1971The probability of winning a game is 1/4. A player expects 6 wins. How many games did they play?
- 21st January 1971A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 22nd January 1971Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 23rd January 1971Write 7/(x - 4) + 5/(x + 3) as a single fraction.
- 24th January 1971y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 25th January 1971In a vector proof you find that vector PQ = a - 2b and vector RS = 4a - 8b. What does this show about PQ and RS?
- 26th January 1971A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 27th January 1971On 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?
- 28th January 1971Simplify sqrt(27) + sqrt(12), giving your answer in the form a sqrt(b).
- 29th January 1971Solve 4x^2 + x - 3 = 0.
- 30th January 1971y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 31st January 1971A cuboid measures 5 cm by 3 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.