Daily Practice · Higher Plus
January 1960 5-a-day
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The batch download puts all 5 tiers' January 1960 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1960
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1960On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 2nd January 1960A car covers 830 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.
- 3rd January 1960Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 4th January 1960A train slows steadily from 16 m/s to rest in 10 seconds. Work out its deceleration.
- 5th January 1960A cuboid measures 8 cm by 7 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th January 1960A bag holds 7 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th January 1960A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 8th January 1960Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
- 9th January 1960f(x) = 4x + 2 and g(x) = 2x + 4. Work out fg(5).
- 10th January 1960y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 11th January 1960The 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.
- 12th January 1960A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 13th January 1960On 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?
- 14th January 1960Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 15th January 1960The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 16th January 1960y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 17th January 1960In 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.
- 18th January 1960The probability of winning a game is 1/4. A player expects 2 wins. How many games did they play?
- 19th January 1960A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 20th January 1960A rectangle is 4 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st January 1960A quadratic sequence starts 14, 31, 56, 89. Work out the second difference, and the coefficient of n^2.
- 22nd January 1960y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 16.
- 23rd January 1960In a vector proof you find that vector PQ = a + 4b and vector RS = 3a + 12b. What does this show about PQ and RS?
- 24th January 1960A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 25th January 1960On 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?
- 26th January 1960Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 27th January 1960Solve x^2 - 9x + 8 > 0.
- 28th January 1960A train slows steadily from 12 m/s to rest in 10 seconds. Work out its deceleration.
- 29th January 1960A cuboid measures 7 cm by 7 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th January 1960A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st January 1960A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?