TI-84 Plus CE lesson 2: The home screen: storing values and avoiding rounding errors

A value you work out in part (a) is usually needed in part (b). This lesson makes storing it a habit, so a rounded number is never typed back in and the final answer is right to 3 significant figures.

Lesson 2 of 12
About 55 minutes
TI-84 Plus CE (OS 5.x)
Free, no sign-in

Objective

Store any value in a letter, use the letters in later calculations and formulas, and explain why rounding too early can change the final answer.

By the end, students can:

store a value with sto→ then alpha and a letter
find the letters printed above the keys (A on math, B on apps, C on prgm, H on ^, R on ×, X on sto→)
type a formula using stored letters and change one value with 2nd enter (ENTRY)
chain calculations with Ans for a repeated percentage change
show a case where a rounded value typed back in gives the wrong 3 s.f. answer

Which courses this lesson suits

IB Maths AA (SL and HL): Papers 2 and 3
IB Maths AI (SL and HL): every paper
A Level Maths (UK and IAL): calculator allowed in every paper

Before you start

Students need lesson 1's habits: the mode screen, QUIT, ANS and ENTRY. Stored letters stay in memory when the calculator is turned off, so old values may be there already: that is the point of step 2.

The key presses, step by step

Every key is shown as it is printed on the calculator, like 2nd or enter. A second function (printed above a key) is 2nd then that key; a menu item is chosen by its number, or by moving to it and pressing enter.

Type 7.25, press sto→, then alpha math (the letter A is printed above math) and enter. The screen shows 7.25→A and the value 7.25.
sto→ writes → on the line. alpha then gives the green letter printed above the next key.
What the screen shows after this step (our drawing of the TI-84 Plus CE screen, not a photo).
Recall it: alpha math (A) enter shows 7.25. A letter can go anywhere a number can: 2A enter gives 14.5 (no × needed).
A letter you never stored is not empty: it holds whatever was stored last time, often from another lesson. Store before you use.
What the screen shows after this step (our drawing of the TI-84 Plus CE screen, not a photo).
Several values on one line: the colon is alpha .. Type 2 sto→ alpha math alpha . (−) 7 sto→ alpha apps alpha . 3 sto→ alpha prgm enter: A = 2, B = −7, C = 3.
Now type the formula once: B² − 4AC enter gives 25, the discriminant of 2x² − 7x + 3.
Change one value later and press 2nd enter (ENTRY) until the formula line is back, then enter: the formula is reused with the new value.
What the screen shows after this step (our drawing of the TI-84 Plus CE screen, not a photo).
Ans chains. A car worth 24000 loses 15% of its value each year. Type 24000 enter, then × 0.85 enter (the line starts Ans*0.85). Each extra enter is one more year: 20400, then 17340, and so on.
Count the presses: the screen keeps every line, so you can check which year you are on.
What the screen shows after this step (our drawing of the TI-84 Plus CE screen, not a photo).
Why store at all? A cylinder has volume 640 cm³ and radius 3.8 cm. The height is 640 ÷ (π × 3.8²). Type 640 ÷ (π × 3.8²), then sto→ alpha ^ (H) and enter on the same line: the screen shows 14.10791739, now stored in H. The surface area 2π × 3.8² + 2π × 3.8 × H is 427.5713011, so 428 cm² to 3 s.f.
With the height rounded to 14.1 and typed back in, the same formula gives 427.3822646: 427 cm². The 3 s.f. answer is wrong.
π is 2nd ^. Rounding errors grow when a rounded value is multiplied by something large.
What the screen shows after this step (our drawing of the TI-84 Plus CE screen, not a photo).

Your turn: check your understanding

Try these straight after the key presses, on your own calculator, before looking at the answers.

Store 4.6 in R (sto→ alpha ×). Use R to work out πR² and 2πR.
Store A = 1, B = −3 and C = −5 on one line. Work out B² − 4AC, then the larger root (−B + √(B² − 4AC)) ÷ (2A).
Now store 2 in B only. Use 2nd enter (ENTRY) to bring back B² − 4AC and press enter. What is the new value?

Show the answers

πR² = 66.5, 2πR = 28.9 (3 s.f.).
B² − 4AC = 29; larger root 4.19 (3 s.f.).
24. Nothing was retyped except the new B.

Exam efficiency

Store every answer you might need again, straight away: a letter takes two key presses.
Write the rounded value in your working, but use the stored one on the calculator.
Use letters that match the question (H for height, R for radius) so you remember what each one holds.
Before a long question, store fresh values: an old letter from another day gives a wrong answer with no warning.

Worked exam-style example

Question. A solid sphere has volume 200 cm³. (a) Find its radius r. (b) Find its surface area. Give your answers to 3 significant figures.

(a) r = ∛(3V ÷ 4π). The cube root is math 4: ∛(. Type ∛(3 × 200 ÷ (4π)) enter: 3.627831679.
What the screen shows after this step (our drawing of the TI-84 Plus CE screen, not a photo).
Store it straight away: sto→ alpha × (R) enter. The line reads Ans→R.
What the screen shows after this step (our drawing of the TI-84 Plus CE screen, not a photo).
(b) 4πR² enter: 165.3880481.
What the screen shows after this step (our drawing of the TI-84 Plus CE screen, not a photo).

What to write down

(a) (4/3)πr³ = 200, so r = ∛(600 ÷ 4π) = 3.63 cm.

(b) Surface area = 4πr² = 165 cm² (using the stored r, not 3.63).

Practice

Do these on your own calculator. Write the answers to 3 significant figures unless the task says otherwise.

Store 2.35 in K (K is alpha (). Work out K³ − 4K.
A cylinder has volume 450 cm³ and radius 3.6 cm. Work out its surface area twice: with the height stored, and with the height rounded to 3 s.f. and typed in. Give both to 3 s.f.
Work out (√7)¹⁰ by typing √(7) enter then Ans^10. Then type 2.65^10. Give both answers to the nearest whole number.
A town has 5000 people and grows by 3% a year. Use an Ans chain to find the population after 5 years, to the nearest whole number.
Store 0.35 in P. Work out P(1 − P)³ to 3 s.f.

Show the practice answers

3.58
Stored: 331 cm². Rounded height: 333 cm². Only the first is right.
16807 (exactly 7⁵) and 17079: rounding √7 to 2.65 puts the answer out by 272.
5796
0.0961

Common mistakes

Pressing sto→ then the key without alpha: you store into the wrong thing or get an error. It is sto→ alpha letter.
Typing the rounded value from part (a) into part (b): use the stored letter.
Using a letter that still holds an old value: store before you use.
Writing calculator syntax as working (Ans→R, 4πR²): write the maths: r = 3.63, S = 4πr² = 165.
Using − for a negative value in A, B or C: −7→B needs (−).

1-minute quick check

Answer these without looking back. Most need no calculation: they check that the key presses have stuck.

Which keys store the answer on the screen in A?
Which key types the colon that separates two commands on one line?
You type B²−4AC and get a strange answer. What should you check?
Which keys bring back the formula line so you can run it with a new value?
Should you write the rounded or the stored value in your working?

Show the quick-check answers

sto→ alpha math enter
alpha .
That A, B and C were stored for this question, not left over from earlier.
2nd enter (ENTRY), pressed until the line appears, then enter
Write the rounded value; keep using the stored one on the calculator.

Teaching this lesson (about 55 minutes)

0–5 min	Starter: the cylinder (step 5) worked two ways on the board. Which answer is right, and why do they differ?
5–15 min	Steps 1–2: storing and recalling, where the letters are on the keys.
15–25 min	Steps 3–4: a formula with stored letters, ENTRY to change one value, and an Ans chain.
25–32 min	Your turn tasks 1–3 in pairs.
32–40 min	Worked example: the sphere, storing r before part (b).
40–52 min	Practice tasks 1–5.
52–55 min	1-minute quick check.

Students need their own TI-84 Plus CE. With a projector, the calculator-skills guides below have a Show on the board view and an animated walkthrough of the key presses.