Daily Practice · Higher Plus
January 1953 5-a-day
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The batch download puts all 5 tiers' January 1953 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1953On 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?
- 2nd January 1953Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.
- 3rd January 1953The point (-6, -2) lies on y = f(x). Write down its image on y = -f(x).
- 4th January 1953y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 5th January 1953A cuboid measures 10 cm by 14 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th January 1953A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th January 1953A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 8th January 1953Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 9th January 1953Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 10th January 1953y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 36.
- 11th January 1953A cuboid measures 5 cm by 11 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th January 1953A bag holds 3 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th January 1953On 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?
- 14th January 1953A rectangle is 27 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th January 1953f(x) = 3x + 4 and g(x) = 6x + 9. Work out fg(6).
- 16th January 1953A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 17th January 1953The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 18th January 1953A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 19th January 1953A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 20th January 1953Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).
- 21st January 1953The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 22nd January 1953y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 23rd January 1953In 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.
- 24th January 1953The probability of winning a game is 3/5. A player expects 24 wins. How many games did they play?
- 25th January 1953On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 26th January 1953A block has mass 830 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th January 1953A quadratic sequence starts 3, 3, 5, 9. Work out the second difference, and the coefficient of n^2.
- 28th January 1953y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 29th January 1953In a vector proof you find that vector PQ = 6a + b and vector RS = 30a + 5b. What does this show about PQ and RS?
- 30th January 1953A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 31st January 1953A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?